# Alexander Schwarz

## Dr.-Ing. Alexander Schwarz

Research » Teaching » Career » Supervised theses » Publications

## Research

Development of mixed finite element formulations for

- the incompressible Navier-Stokes equations
- isotropic und anisotropic hyperelasticity
- elasto-(visco)plastic material behaviour at finite strains
- time-dependent problems
- fluid-structure-interaction (FSI)
- theory of porous media (TPM)

## Teaching

- Technische Mechanik 1 (Engineering Mechanics 1: Statics / Elastostatics I)

- Technische Mechanik 2 (Engineering Mechanics 2: Elastostatics II / Hydromechanics)

- Technische Mechanik 3 (Engineering Mechanics 3: Dynamics)

- Bauinformatik (Computer Sciences for Civil Engineers)

- Finite Element Method: Foundations

- Nonlinear Finite Element Method

- Computational Inelasticity

- Multiphase materials

- Höhere Mechanik (Advanced Mechanics)

## Career

1995 | High-school diploma (Abitur), Hohenlohe Gymnasium Öhringen |

1995- 1996 | Civilian service |

1996- 2004 | Engineering studies (civil engineering), University of Duisburg-Essen and University of Adelaide |

2004 | Stipendiary of Deutschen Akademischen Austausch Dienst (DAAD) |

2004 | Diploma thesis at University of Adelaide, Australia, School of Mechanical Engineering. Title: "Investigations to Second Order Derivatives within Meshfree Approximations" |

2005- 2009 | Research assistant, Institute of Mechanics, Faculty of Engineering, Department Civil Engineering, University of Duisburg-Essen |

2009 | Doctoral degree (Dr.-Ing.), University Duisburg Essen, Title: "Least- Squares Mixed Finite Elements for Solid Mechanics" |

2010 | "Akademischer Rat", Institute of Mechanics, University Duisburg- Essen |

2011 | Director of the international master degree course Computational Mechanics |

2013 | Academic senior councilor at the Institute of Mechanics, University Duisburg- Essen |

## Supervised theses

- Kugai, S. [2017], "Investigation of mixed least-squares finite element formulations for the incompressible Navier-Stokes equations based on quadrilateral and hexahedral elements.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Levermann, J. [2016], "Investigation of Newmark time integration schemes for the incompressible Navier-Stokes fluid flow in least-squares finite element methods.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Endrikat, L. [2016], " Mixed Galerkin finite element method in 2D und 3D for the incompressible Navier-Stokes equations.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Depenbrock, R. [2016], " On a three- dimensional mixed least-squares finite element formulation interpolating stresses and displacements in H$^1$($\mathcal{B}$) under consideration of small strains.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Averweg, S. [2016], "Least-squares FEM with Lagrange interpolation in 2D and 3D for the S-V-P formulation of the incompressible Navier-Stokes equations. ", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Maassen, S. [2016], "On a geometrically nonlinear least-squares finite element formulation for numerical simulations of piezoelectrical coupling phenomenons. ", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Umar, O. [2015], "Mixed Galerkin finite element formulation for the incompressible Stokes/Navier-Stokes equation for newtonian - and non newtonian fluids.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Igelbüscher, M. [2015], Comparsion of geometrically lienar and nonlinear finite element formulations of elasto-plasticity.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Bohne, F. [2015], "A velocity-vorticity-pressure least-squares finite element formulation of stationary and instationary laminar newtonian fluid flows.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Stenchlik, D. [2015], "Implementation and comparsion of mixed least-squares finite elements for the solution of dynamic problems in incompressible linear elasticity.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Kugai, S. [2015], "Implementierung und Vergleich der Galerkin und Least-Squares FEM anhand von Transportgleichungen.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Averweg, S. [2014], "Comparsion and implementation of least-squares and Kriging approximation approaches.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Endrikat, L. [2014], "Implementation and investigation of hexahedral finite elements of different polynomial order.", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Viebahn, N. [2014], "Implementation of higher order finite elementr for quasi-incompressible (non-) linear elasticity in AceGen.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Nisters, C. [2013], "Mixed finite element implementation of a two-dimensional strain gradient elasticity model", Master thesis, Institut of Mechancs, Dept. of civil engineering, University Duisburg-Essen.

- Serdas, S. [2012], "Comparison of stabilization techniques for mixed Galerkin FEM in the field of transport and flow problems.", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.
- Romanski, L. [2011], "Konstruktion und Implementierung von skalar- und vektorwertigen Ansatzfunktionen höherer Ordnung", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Saubke, V. [2011], "Numerische Untersuchungen von Viereckselementen für konforme Diskretisierungen in H(div) ", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Steeger, K. [2010], "A weighted mixed Least-Squares finite element formulation solving linear elastodynamic problems", Master thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Steeger, K. [2008], "A least-squares mixed finite element formulation based on the St. Venant-Kirchhoff material law", Bachelor thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Kampen, A. [2007], "Gemischte Least-Squares Finite Elemente für lineare, inkompressible Elastizität", Diploma thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

- Bujna, G. [2006], "Berechnung von Raumluftströmungen - Konvergenzstudien strömungsmechanischer Probleme mit dem Programmsystem FLUENT", Diploma thesis, Institut of Mechanics, Dept. of civil engineering, University Duisburg-Essen.

## Publications

Schwarz A, Bluhm J and Schröder J (accepted (2019)), "A finite element formulation for freezing and thawing processes of ice within the framework of the TPM", In Research and Applications in Structural Engineering, Mechanics & Computation. Cape Town, South Africa Taylor & Francis Group.
[BibTeX] |

BibTeX:
@incollection{SchBluSch:2019:afe, author = {J. Schröder and J. Bluhm and A. Schwarz}, editor = {A. Zingoni}, title = {A finite element formulation for freezing and thawing processes of ice within the framework of the TPM}, booktitle = {Research and Applications in Structural Engineering, Mechanics & Computation}, publisher = {Taylor & Francis Group}, year = {2019} } |

Averweg S, Schwarz A, Nisters C and Schröder J (2018), "Implicit time discretization schemes for least-squares finite element formulations to model incompressible flows", Proceedings in Applied Mathematics and Mechanics. Vol. 18, pp. e201800166 (2 pages).
[BibTeX] |

BibTeX:
@article{AveSchNisSch:2018:itd, author = {S. Averweg and A. Schwarz and C. Nisters and J. Schröder}, title = {Implicit time discretization schemes for least-squares finite element formulations to model incompressible flows}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2018}, volume = {18}, pages = {e201800166 (2 pages)} } |

Igelbüscher M, Schwarz A, Steeger K and Schröder J (2018), "Modified mixed least-squares finite element formulations for small and finite strain plasticity", International Journal for Numerical Methods in Engineering. Vol. 117, pp. 141-160.
[BibTeX] |

BibTeX:
@article{IgeSchSteSch:2018:mml, author = {Igelbüscher, M. and Schwarz, A. and Steeger, K. and Schröder, J.}, title = {Modified mixed least-squares finite element formulations for small and finite strain plasticity}, journal = {International Journal for Numerical Methods in Engineering}, year = {2018}, volume = {117}, pages = {141--160} } |

Nisters C and Schwarz A (2018), "Efficient stress--velocity least-squares finite element formulations for the incompressible Navier--Stokes equations", Computer Methods in Applied Mechanics and Engineering. Vol. 341, pp. 333 - 359.
[BibTeX] |

BibTeX:
@article{NisSch:2018:esv, author = {C. Nisters and A. Schwarz}, title = {Efficient stress--velocity least-squares finite element formulations for the incompressible Navier--Stokes equations}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2018}, volume = {341}, pages = {333 - 359} } |

Nisters C, Schwarz A, Averweg S and Schröder J (2018), "Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains", In Advances in Mechanics of Materials and Structural Analysis: In Honor of Reinhold Kienzler. , pp. 261-279. Springer International Publishing.
[BibTeX] |

BibTeX:
@incollection{NisSchAverSch:2017:roa, author = {Nisters, Carina and Schwarz, Alexander and Averweg, Solveigh and Schröder, Jörg}, editor = {Altenbach, Holm and Jablonski, Frank and Müller, Wolfgang H. and Naumenko, Konstantin and Schneider, Patrick}, title = {Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains}, booktitle = {Advances in Mechanics of Materials and Structural Analysis: In Honor of Reinhold Kienzler}, publisher = {Springer International Publishing}, year = {2018}, pages = {261--279} } |

Schwarz A, Averweg S, Nisters C and Schröder J (2018), "A fluid-structure interaction approach with inherently fulfilled coupling conditions", Proceedings in Applied Mathematics and Mechanics. Vol. 18, pp. e201800183 (2 pages).
[BibTeX] |

BibTeX:
@article{SchAveNisSch:2018:afs, author = {A. Schwarz and S. Averweg and and C. Nisters and J. Schröder}, title = {A fluid-structure interaction approach with inherently fulfilled coupling conditions}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2018}, volume = {18}, pages = {e201800183 (2 pages)} } |

Schwarz A and Dwight R (2018), "Data Assimilation for Navier-Stokes using the Least-Squares Finite-Element Method", International Journal for Uncertainty Quantification. Vol. 8(5), pp. 383-403.
[BibTeX] |

BibTeX:
@article{SchDwi:2018:daf, author = {Schwarz, A. and Dwight, R.}, title = {Data Assimilation for Navier-Stokes using the Least-Squares Finite-Element Method}, journal = {International Journal for Uncertainty Quantification}, year = {2018}, volume = {8}, number = {5}, pages = {383--403} } |

Schwarz A, Nickaeen M, Serdas S, Nisters C, Ouazzi A, Schröder J and Turek S (2018), "A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations", International Journal of Computational Science and Engineering. Vol. 17(1), pp. 80-97.
[BibTeX] |

BibTeX:
@article{SchNicSerNisOuaSchTur:2018:acs, author = {A. Schwarz and M. Nickaeen and S. Serdas and Carina Nisters and A. Ouazzi and J. Schröder and S. Turek}, title = {A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations}, journal = {International Journal of Computational Science and Engineering}, year = {2018}, volume = {17}, number = {1}, pages = {80--97} } |

Schwarz A, Nisters C, Averweg S and Schröder J (2018), "Stress-Velocity Mixed Least-Squares FEMs for the Time-Dependent Incompressible Navier-Stokes Equations", In Large-Scale Scientific Computing. Cham , pp. 137-144. Springer International Publishing.
[BibTeX] |

BibTeX:
@inproceedings{SchNisAveSch:2017:svm, author = {Schwarz, Alexander and Nisters, Carina and Averweg, Solveigh and Schröder, Jörg}, editor = {Lirkov, Ivan and Margenov, Svetozar}, title = {Stress-Velocity Mixed Least-Squares FEMs for the Time-Dependent Incompressible Navier-Stokes Equations}, booktitle = {Large-Scale Scientific Computing}, publisher = {Springer International Publishing}, year = {2018}, pages = {137--144} } |

Schwarz A, Steeger K, Igelbüscher M and Schröder J (2018), "Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures", International Journal for Numerical Methods in Engineering. Vol. 115, pp. 1138-1153.
[BibTeX] |

BibTeX:
@article{SchSteIgeSch:2018:daf, author = {Schwarz, A. and Steeger, K. and Igelbüscher, M. and Schröder, J.}, title = {Different approaches for mixed LSFEMs in hyperelasticity: Application of logarithmic deformation measures}, journal = {International Journal for Numerical Methods in Engineering}, year = {2018}, volume = {115}, pages = {1138--1153} } |

Igelbüscher M, Schwarz A, Steeger K and Schröder J (2017), "Remarks on a modified mixed least-squares finite element formulation for small strain elasto-plasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 17, pp. 311-312.
[BibTeX] |

BibTeX:
@article{IgeSchSteSch:2017:roa, author = {Igelbüscher, M. and Schwarz, A. and Steeger, K. and Schröder, J.}, title = {Remarks on a modified mixed least-squares finite element formulation for small strain elasto-plasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2017}, volume = {17}, pages = {311--312} } |

Nisters C, Schwarz A and Schröder J (2017), "Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 17, pp. 631-632.
[BibTeX] |

BibTeX:
@article{NisSchSch:2017:ios, author = {C. Nisters and A. Schwarz and J. Schröder}, title = {Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2017}, volume = {17}, pages = {631--632} } |

Schröder J, Igelbüscher M, Schwarz A and Starke G (2017), "A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity", Computer Methods in Applied Mechanics and Engineering. Vol. 317, pp. 400-418.
[BibTeX] |

BibTeX:
@article{SchIgeSchSta:2016:aph, author = {J. Schröder and M. Igelbüscher and A. Schwarz and G. Starke}, title = {A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2017}, volume = {317}, pages = {400--418} } |

Igelbüscher M, Schröder J and Schwarz A (2016), "On the performance of the Prange-Hellinger-Reissner finite element formulation for elasto-plasticity at small strains", Proceedings in Applied Mathematics and Mechanics. Vol. 16, pp. 203-204.
[BibTeX] |

BibTeX:
@article{IgeSchSch:16:otp, author = {M. Igelbüscher and J. Schröder and A. Schwarz}, title = {On the performance of the Prange-Hellinger-Reissner finite element formulation for elasto-plasticity at small strains}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2016}, volume = {16}, pages = {203-204} } |

Schwarz A, Steeger K, Igelbüscher M and Schröder J (2016), "Comparison of different least-squares mixed finite element formulations for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 16, pp. 239-240.
[BibTeX] |

BibTeX:
@article{SchSteIgeSch:16:cod, author = {A. Schwarz and K. Steeger and M. Igelbüscher and J. Schröder}, title = {Comparison of different least-squares mixed finite element formulations for hyperelasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2016}, volume = {16}, pages = {239-240} } |

Schröder J, Turek S and Schwarz A (2016), "Alles im Fluss -- Simulationstechniken der Strömungsmechanik in der Materials Chain", In Essener Unikate 48: Materials Chain -- Forschung aus dem UA Ruhr-Profilschwerpunkt. Universität Duisburg--Essen.
[BibTeX] |

BibTeX:
@incollection{SchTurSch:2016:aif, author = {J. Schröder and S. Turek and A. Schwarz}, title = {Alles im Fluss -- Simulationstechniken der Strömungsmechanik in der Materials Chain}, booktitle = {Essener Unikate 48: Materials Chain -- Forschung aus dem UA Ruhr-Profilschwerpunkt}, publisher = {Universität Duisburg--Essen}, year = {2016} } |

Nisters C, Schwarz A, Steeger K and Schröder J (2015), "A stress-velocity least-squares mixed finite element formulation for incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 15(1), pp. 217-218.
[BibTeX] |

BibTeX:
@article{NisSchSteSch:2015:asv, author = {C. Nisters and A. Schwarz and K. Steeger and J. Schröder}, title = {A stress-velocity least-squares mixed finite element formulation for incompressible elastodynamics}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2015}, volume = {15}, number = {1}, pages = {217--218} } |

Schwarz A, Steeger K and Schröder J (2015), "Weighted overconstrained least-squares mixed finite elements for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 15, pp. 227-228.
[BibTeX] |

BibTeX:
@article{SchSteSch:2015:wol, author = {A. Schwarz and K. Steeger and J. Schröder}, title = {Weighted overconstrained least-squares mixed finite elements for hyperelasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2015}, volume = {15}, pages = {227--228} } |

Steeger K, Schröder J and Schwarz A (2015), "Comparison of a mixed least-squares formulation using different approximation spaces", Proceedings in Applied Mathematics and Mechanics. Vol. 15, pp. 233-234.
[BibTeX] |

BibTeX:
@article{SteSchSchStaMue:2014:coa, author = {K. Steeger and J. Schröder and A. Schwarz}, title = {Comparison of a mixed least-squares formulation using different approximation spaces}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2015}, volume = {15}, pages = {233--234} } |

Müller B, Starke G, Schwarz A and Schröder J (2014), "A first-order system least squares method for hyperelasticity", SIAM Journal on Scientific Computing. Vol. 36, pp. 795-816.
[BibTeX] |

BibTeX:
@article{MueStaSchSch:2014:afo, author = {B. Müller and G. Starke and A. Schwarz and J. Schröder}, title = {A first-order system least squares method for hyperelasticity}, journal = {SIAM Journal on Scientific Computing}, year = {2014}, volume = {36}, pages = {795--816} } |

Schwarz A, Steeger K and Schröder J (2014), "Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity", Computational Mechanics. Vol. 54(1), pp. 603-612.
[BibTeX] |

BibTeX:
@article{SchSteSch:2014:wol, author = {A. Schwarz and K. Steeger and J. Schröder}, title = {Weighted overconstrained least-squares mixed finite elements for static and dynamic problems in quasi-incompressible elasticity}, journal = {Computational Mechanics}, year = {2014}, volume = {54}, number = {1}, pages = {603--612} } |

Schwarz A, Steeger K, Schröder J, Starke G and Müller B (2014), "An improved mixed finite element based on a modified least-squares formulation for hyperelasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 243-244.
[BibTeX] |

BibTeX:
@article{SchSteSchStaMue:2014:aim, author = {A. Schwarz and K. Steeger and J. Schröder and G. Starke and B. Müller}, title = {An improved mixed finite element based on a modified least-squares formulation for hyperelasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, volume = {14}, pages = {243--244} } |

Serdas S, Schwarz A, Schröder J, Turek S, Ouazzi A and Nickaeen M (2014), "Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 623-624.
[BibTeX] |

BibTeX:
@article{SerSchSchTurOuaNic:2014:aim, author = {S. Serdas and A. Schwarz and J. Schröder and S. Turek and A. Ouazzi and M. Nickaeen}, title = {Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, volume = {14}, pages = {623--624} } |

Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2014), "On a least-squares formulation for hyperelastic, transversely isotropic problems", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 247-248.
[BibTeX] |

BibTeX:
@article{SteSchSchStaMue:2014:oal, author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller}, title = {On a least-squares formulation for hyperelastic, transversely isotropic problems}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, volume = {14}, pages = {247--248} } |

Kiefer B, Niederhaus C, Balzani D, Bobisch CA, Gerharz E, Kruggel-Emden H, Schwarz A, Thielbörger P and Weiss GN (2013), "Anreizsysteme--Eine Möglichkeit zur Verbesserung der universitären Lehre", Journal für Hochschuldidaktik. , pp. 1-2.
[BibTeX] |

BibTeX:
@article{kiefer2013anreizsysteme, author = {Kiefer, Björn and Niederhaus, Constanze and Balzani, Daniel and Bobisch, Christian A and Gerharz, Eva and Kruggel-Emden, Harald and Schwarz, Alexander and Thielbörger, Pierre and Weiss, Gregor NF}, title = {Anreizsysteme--Eine Möglichkeit zur Verbesserung der universitären Lehre}, journal = {Journal für Hochschuldidaktik}, year = {2013}, pages = {1--2} } |

Schwarz A, Schröder J, Serdas S, Turek S, Ouazzi A and Nickaeen M (2013), "Performance aspects of a mixed s-v LSFEM for the incompressible Navier-Stokes equations with improved mass conservation", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 513-514.
[BibTeX] |

BibTeX:
@article{SchSchSerTurOuaNic:2013:pao, author = {A. Schwarz and J. Schröder and S. Serdas and S. Turek and A. Ouazzi and M. Nickaeen}, title = {Performance aspects of a mixed s-v LSFEM for the incompressible Navier-Stokes equations with improved mass conservation}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2013}, volume = {13}, pages = {513--514} } |

Serdas S, Schwarz A, Schröder J, Turek S, Ouazzi A and Nickaeen M (2013), "Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 310-302.
[BibTeX] |

BibTeX:
@article{SerSchSchTurOuaNic:2013:ioh, author = {S. Serdas and A. Schwarz and J. Schröder and S. Turek and A. Ouazzi and M. Nickaeen}, title = {Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2013}, volume = {13}, pages = {310--302} } |

Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2013), "Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models", Proceedings in Applied Mathematics and Mechanics. Vol. 13, pp. 97-98.
[BibTeX] |

BibTeX:
@article{SteSchSchStaMue:2013:shp, author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller}, title = {Comparison of geometrically nonlinear LSFEM formulations based on different hyperelastic models}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2013}, volume = {13}, pages = {97--98} } |

Wriggers P, Schröder J and Schwarz A (2013), "A finite element method for contact using a third medium", Computational Mechanics. Vol. 52, pp. 837-847.
[BibTeX] |

BibTeX:
@article{WriSchSch:2013:afe, author = {P. Wriggers and J. Schröder and A. Schwarz}, title = {A finite element method for contact using a third medium}, journal = {Computational Mechanics}, year = {2013}, volume = {52}, pages = {837--847} } |

Schwarz A and Schröder J (2012), "On a reduced mixed s-v least-squares finite element formulation for the incompressible Navier-Stokes equations", Proceedings in Applied Mathematics and Mechanics. Vol. 12, pp. 455-456.
[BibTeX] |

BibTeX:
@article{SchSch:2012:oar, author = {A. Schwarz and J. Schröder}, title = {On a reduced mixed s-v least-squares finite element formulation for the incompressible Navier-Stokes equations}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2012}, volume = {12}, pages = {455--456} } |

Schwarz A, Schröder J, Starke G and Steeger K (2012), "Least-squares mixed finite elements for hyperelastic material models", In Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers. , pp. 470-472.
[BibTeX] |

BibTeX:
@inproceedings{SchSchStaSte:2012:lmf, author = {A. Schwarz and J. Schröder and G. Starke and K. Steeger}, title = {Least-squares mixed finite elements for hyperelastic material models}, booktitle = {Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers}, year = {2012}, pages = {470--472} } |

Starke G, Müller B, Schwarz A and Schröder J (2012), "Stress-displacement least squares mixed finite element approximation for hyperelastic materials", In Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers. , pp. 467-469.
[BibTeX] |

BibTeX:
@inproceedings{StaMueSchSch:2012:sls, author = {G. Starke and B. Müller and A. Schwarz and J. Schröder}, title = {Stress-displacement least squares mixed finite element approximation for hyperelastic materials}, booktitle = {Report of the Workshop 1207 at the ``Mathematisches Forschungsinstitut Oberwolfach'' entitled ``Advanced Computational Engineering'', organized by O. Allix, C. Carstensen, J. Schröder, P. Wriggers}, year = {2012}, pages = {467--469} } |

Steeger K, Schwarz A, Schröder J, Starke G and Müller B (2012), "Solving hyperelastic problems using mixed LSFEM", Proceedings in Applied Mathematics and Mechanics. Vol. 12, pp. 215-216.
[BibTeX] |

BibTeX:
@article{SteSchSchStaMue:2012:shp, author = {K. Steeger and A. Schwarz and J. Schröder and G. Starke and B. Müller}, title = {Solving hyperelastic problems using mixed LSFEM}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2012}, volume = {12}, pages = {215--216} } |

Schwarz A and Schröder J (2011), "A mixed least-squares formulation of the Navier-Stokes equations for incompressible Newtonian fluid flow", Proceedings in Applied Mathematics and Mechanics. Vol. 11, pp. 589-590.
[BibTeX] |

BibTeX:
@article{SchSch:2011:aml, author = {A. Schwarz and J. Schröder}, title = {A mixed least-squares formulation of the Navier-Stokes equations for incompressible Newtonian fluid flow}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2011}, volume = {11}, pages = {589--590} } |

Starke G, Schwarz A and Schröder J (2011), "Analysis of a modified First-Order System Least Squares Method for linear Elasticity with improved Momentum Balance", SIAM Journal on Numerical Analysis. Vol. 49, pp. 1006-1022.
[BibTeX] |

BibTeX:
@article{StaSchSch:2011:aoa, author = {G. Starke and A. Schwarz and J. Schröder}, title = {Analysis of a modified First-Order System Least Squares Method for linear Elasticity with improved Momentum Balance}, journal = {SIAM Journal on Numerical Analysis}, year = {2011}, volume = {49}, pages = {1006-1022} } |

Steeger K, Schwarz A and Schröder J (2011), "A weighted least-squares mixed finite element formulation for quasi-incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 11(1), pp. 287-288.
[BibTeX] |

BibTeX:
@article{SteSchSch:2011:awl, author = {K. Steeger and A. Schwarz and J. Schröder}, title = {A weighted least-squares mixed finite element formulation for quasi-incompressible elastodynamics}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2011}, volume = {11}, number = {1}, pages = {287--288} } |

Schwarz A, Schröder J and Starke G (2010), "A modified least-squares mixed finite element with improved momentum balance", International Journal for Numerical Methods in Engineering. Vol. 81, pp. 286-306.
[BibTeX] |

BibTeX:
@article{SchSchSta:2010:aml, author = {A. Schwarz and J. Schröder and G. Starke}, title = {A modified least-squares mixed finite element with improved momentum balance}, journal = {International Journal for Numerical Methods in Engineering}, year = {2010}, volume = {81}, pages = {286--306} } |

Steeger K, Schwarz A and Schröder J (2010), "A least-squares mixed finite element for quasi-incompressible elastodynamics", Proceedings in Applied Mathematics and Mechanics. Vol. 10(1), pp. 219-220.
[BibTeX] |

BibTeX:
@article{SteSchSch:2010:als, author = {K. Steeger and A. Schwarz and J. Schröder}, title = {A least-squares mixed finite element for quasi-incompressible elastodynamics}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2010}, volume = {10}, number = {1}, pages = {219--220} } |

Schwarz A (2009), "Least-Squares Mixed Finite Elements for Solid Mechanics". Thesis at: University Duisburg-Essen.
[BibTeX] |

BibTeX:
@phdthesis{Sch:2009:lsm, author = {Schwarz, A.}, title = {Least-Squares Mixed Finite Elements for Solid Mechanics}, school = {University Duisburg-Essen}, year = {2009} } |

Schwarz A and Schröder J (2009), "An asymmetric least-squares mixed finite element for elasto-plasticity at small strains", Proceedings in Applied Mathematics and Mechanics. Vol. 9, pp. 235-236.
[BibTeX] |

BibTeX:
@article{SchSch:2009:aal, author = {A. Schwarz and J. Schröder}, title = {An asymmetric least-squares mixed finite element for elasto-plasticity at small strains}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2009}, volume = {9}, pages = {235--236} } |

Schwarz A and Schröder J (2009), "A modified least-squares finite element formulation for small strain plasticity", In Proceedings of ICCSM 2009.
[BibTeX] |

BibTeX:
@inproceedings{SchSch:2009:aml, author = {A. Schwarz and J. Schröder}, title = {A modified least-squares finite element formulation for small strain plasticity}, booktitle = {Proceedings of ICCSM 2009}, year = {2009} } |

Schwarz A, Schröder J and Starke G (2009), "Least-squares mixed finite elements for small strain elasto-viscoplasticity", International Journal for Numerical Methods in Engineering. Vol. 77, pp. 1351-1370.
[BibTeX] |

BibTeX:
@article{SchSchSta:2009:lsm, author = {A. Schwarz and J. Schröder and G. Starke}, title = {Least-squares mixed finite elements for small strain elasto-viscoplasticity}, journal = {International Journal for Numerical Methods in Engineering}, year = {2009}, volume = {77}, pages = {1351--1370} } |

Schwarz A, Schröder J and Steeger K (2009), "A modified least-squares Finite Element Formulation for Small Strain Plasticity", In Proceedings of the International Congress of Croatian Society of Mechanics (ICCSM), 2009.
[BibTeX] |

BibTeX:
@conference{SchSchSte:2011:amls, author = {A. Schwarz and J. Schröder and K. Steeger}, title = {A modified least-squares Finite Element Formulation for Small Strain Plasticity}, booktitle = {Proceedings of the International Congress of Croatian Society of Mechanics (ICCSM), 2009}, year = {2009} } |

Schwarz A, Kampen A and Schröder J (2008), "On the construction of Raviart--Thomas finite element spaces". Thesis at: Institut für Mechanik, Universität Duisburg-Essen. (39)
[BibTeX] |

BibTeX:
@techreport{SchKamSch:2008:otc, author = {A. Schwarz and A. Kampen and J. Schröder}, title = {On the construction of Raviart--Thomas finite element spaces}, school = {Institut für Mechanik, Universität Duisburg-Essen}, year = {2008}, number = {39} } |

Schwarz A and Schröder J (2008), "An asymmetric mixed finite element for incompressible elasticity based on a modified least-squares formulation", Proceedings in Applied Mathematics and Mechanics. Vol. 8, pp. 10341-10342.
[BibTeX] |

BibTeX:
@article{SchSch:2008:aam, author = {A. Schwarz and J. Schröder}, title = {An asymmetric mixed finite element for incompressible elasticity based on a modified least-squares formulation}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2008}, volume = {8}, pages = {10341--10342} } |

Ricken T, Schwarz A and Bluhm J (2007), "A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth", Computational Materials Science. Vol. 39(1), pp. 124-136.
[BibTeX] |

BibTeX:
@article{RicSchBlu:2007:atmotibtwatsabig, author = {Tim Ricken and Alexander Schwarz and Joachim Bluhm}, title = {A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth}, journal = {Computational Materials Science}, year = {2007}, volume = {39}, number = {1}, pages = {124--136} } |

Schwarz A and Schröder J (2007), "Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 7, pp. 4040043-4040044.
[BibTeX] |

BibTeX:
@article{SchSch:2007:lmf, author = {A. Schwarz and J. Schröder}, title = {Least-squares mixed finite elements with applications to anisotropic elasticity and viscoplasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {4040043-4040044} } |

Ricken T, Schwarz A and Bluhm J (2006), "A Triphasic Theory for Growth in Biological Tissue – Basics and Applications", Materialwissenschaft und Werkstofftechnik. Vol. 37(6), pp. 446-456.
[BibTeX] |

BibTeX:
@article{RicSchBlu:2006:attfgibtbaa, author = {T. Ricken and A. Schwarz and J. Bluhm}, title = {A Triphasic Theory for Growth in Biological Tissue – Basics and Applications}, journal = {Materialwissenschaft und Werkstofftechnik}, year = {2006}, volume = {37}, number = {6}, pages = {446--456} } |

Schwarz A and Schröder J (2006), "A least square mixed finite element for plane elasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 6, pp. 265-266.
[BibTeX] |

BibTeX:
@article{SchSch:2006:als, author = {A. Schwarz and J. Schröder}, title = {A least square mixed finite element for plane elasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2006}, volume = {6}, pages = {265--266} } |

Schwarz A (2004), "Investigations to Second Order Derivatives within Meshfree Approximations". Thesis at: Institut für Mechanik, Universität Duisburg-Essen. (Diplomarbeit)
[BibTeX] |

BibTeX:
@techreport{Sch:2004:its, author = {A. Schwarz}, title = {Investigations to Second Order Derivatives within Meshfree Approximations}, school = {Institut für Mechanik, Universität Duisburg-Essen}, year = {2004}, number = {Diplomarbeit} } |

Stand: 30.04.2019