# Alexander Schwarz

## Forschung

Entwicklung gemischter finiter Elementformulierungen für

• die inkompressiblen Navier-Stokes Gleichungen
• isotrope und anisotrope Hyperelastizität
• elasto-(visko)plastisches Materialverhalten bei finiten Deformationen
• zeitabhängige Probleme
• Fluid-Struktur-Interaktion (FSI)
• Theorie poröser Medien (TPM)

## Lehre

• Technische Mechanik 1
• Technische Mechanik 2
• Technische Mechanik 3
• Bauinformatik
• Finite Element Method: Foundations
• Nonlinear Finite Element Methods
• Computational Inelasticity
• Multiphase Materials
• Höhere Mechanik

## Werdegang

 1995 Abitur am Hohenlohe Gymnasium Öhringen 1995- 1996 Zivildienst 1996- 2004 Studium Bauingenieurwesen an der Universität Essen und an der University of Adelaide 2004 Stipendiat der Deutschen Akademischen Austausch Dienstes 2004 Diplomarbeit an der University of Adelaide, Australia, School of Mechanical Engineering. Titel der Arbeit: "Investigations to Second Order Derivatives within Meshfree Approximations" 2005- 2009 Wissenschaftlicher Mitarbeiter am Institut für Mechanik, Universität Duisburg- Essen 2009 Promotion zum Dr.- Ing. an der Universität Duisburg Essen. Titel der Arbeit: "Least- Squares Mixed Finite Elements for Solid Mechanics" 2010 Akademischer Rat am Institut für Mechanik, Universität Duisburg- Essen 2011 Kursdirektor des internationalen Master- Studienganges Computational Mechanics 2013 Akademischer Oberrat am Institut für Mechanik, Universität Duisburg-Essen

## Betreute Abschlussarbeiten

• Kugai, S. [2017], "Investigation of mixed least-squares finite element formulations for the incompressible Navier-Stokes equations based on quadrilateral and hexahedral elements.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Levermann, J. [2016], "Investigation of Newmark time integration schemes for the incompressible Navier-Stokes fluid flow in least-squares finite element methods.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Endrikat, L. [2016], " Mixed Galerkin finite element method in 2D und 3D for the incompressible Navier-Stokes equations.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität 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.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität 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. ", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Maassen, S. [2016], "On a geometrically nonlinear least-squares finite element formulation for numerical simulations of piezoelectrical coupling phenomenons. ", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Umar, O. [2015], "Mixed Galerkin finite element formulation for the incompressible Stokes/Navier-Stokes equation for newtonian - and non newtonian fluids.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Igelbüscher, M. [2015], Comparsion of geometrically lienar and nonlinear finite element formulations of elasto-plasticity.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Bohne, F. [2015], "A velocity-vorticity-pressure least-squares finite element formulation of stationary and instationary laminar newtonian fluid flows.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Stenchlik, D. [2015], "Implementation and comparsion of mixed least-squares finite elements for the solution of dynamic problems in incompressible linear elasticity.", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

• Kugai, S. [2015], "Implementierung und Vergleich der Galerkin und Least-Squares FEM anhand von Transportgleichungen.", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Averweg, S. [2014], "Comparsion and implementation of least-squares and Kriging approximation approaches.", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Endrikat, L. [2014], "Implementation and investigation of hexahedral finite elements of different polynomial order.", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Viebahn, N. [2014], "Implementation of higher order finite elementr for quasi-incompressible (non-) linear elasticity in AceGen.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen
• Nisters, C. [2013], "Mixed finite element implementation of a two-dimensional strain gradient elasticity model", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen
• Serdas, S. [2012], "Comparison of stabilization techniques for mixed Galerkin FEM in the field of transport and flow problems.", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen
• Romanski, L. [2011], "Konstruktion und Implementierung von skalar- und vektorwertigen Ansatzfunktionen höherer Ordnung", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Saubke, V. [2011], "Numerische Untersuchungen von Viereckselementen für konforme Diskretisierungen in H(div) ", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Steeger, K. [2010], "A weighted mixed Least-Squares finite element formulation solving linear elastodynamic problems", Masterarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Steeger, K. [2008], "A least-squares mixed finite element formulation based on the St. Venant-Kirchhoff material law", Bachelorarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Kampen, A. [2007], "Gemischte Least-Squares Finite Elemente für lineare, inkompressible Elastizität", Diplomarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.
• Bujna, G. [2006], "Berechnung von Raumluftströmungen - Konvergenzstudien strömungsmechanischer Probleme mit dem Programmsystem FLUENT", Diplomarbeit, Institut für Mechanik, Abt. Bauwissenschaften, Universität Duisburg-Essen.

## Publikationen

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 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

## Dr.-Ing. Alexander Schwarz

Tel. +49(0)201/183-2681
Fax +49(0)201/183-2680
Raum V15 S06 D87
alexander.schwarz@uni-due.de