Gerhard Starke - Publications

  • Weakly Symmetric Stress Equilibration and A Posteriori Error Estimation for Linear Elasticity (jointly with Fleurianne Bertrand, Bernhard Kober and Marcel Moldenhauer), Numerical Methods for Partial Differential Equations (2021) DOI:10.1002/num.22741
  • A Posteriori Error Estimates by Weakly Symmetric Stress Reconstruction for the Biot Problem (jointly with Fleurianne Bertrand), Computers and Mathematics with Applications (2020) DOI:10.1016/j.camwa.2020.10.011
  • Weakly Symmetric Stress Equilibration for Hyperelastic Material Models (jointly with Fleurianne Bertrand and Marcel Moldenhauer), GAMM-Mitteilungen 43 (2020) e202000007
  • Strong vs. Weak Symmetry in Stress-Based Mixed Finite Element Methods for Linear Elasticity (jointly with Bernhard Kober), In: Numerical Mathematics and Advanced Applications ENUMATH 2017 (F. A. Radu et al., eds.), Lecture Notes in Computational Science and Engineering 126, Springer-Verlag, 2019, pp. 323-333
  • A Posteriori Error Estimation for Planar Linear Elasticity by Stress Reconstruction (jointly with Fleurianne Bertrand and Marcel Moldenhauer), Computational Methods in Applied Mathematics 19 (2019), 663-679
  • An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates (jointly with Philipp Bringmann and Carsten Carstensen), SIAM Journal on Numerical Analysis 56 (2018), 428-447
  • A Prange-Hellinger-Reissner Type Finite Element Formulation for Small Strain Elasto-Plasticity (jointly with Jörg Schröder, Maximilian Igelbüscher and Alexander Schwarz), Computer Methods in Applied Mechanics and Engineering 317 (2017), 400-418
  • An Adaptive Least-Squares Mixed Finite Element Method for the Signorini Problem (jointly with Rolf Krause and Benjamin Müller), Numerical Methods for Partial Differential Equations 33 (2017), 276-289
  • Parametric Raviart-Thomas Elements for Mixed Methods on Domains with Curved Surfaces (jointly with Fleurianne Bertrand), SIAM Journal on Numerical Analysis 54 (2016), 3648-3667
  • Stress-Based Finite Element Methods in Linear and Nonlinear Solid Mechanics (jointly with Benjamin Müller), In: Advanced Computational Engineering (Jörg Schröder, Peter Wriggers, eds.), CISM International Centre for Mechanical Sciences Vol. 566, Springer-Verlag, 2016, pp. 69-104
  • Dev-Div- and Devsym-Devcurl-Inequalities for Incompatible Square Tensor Fields with Mixed Boundary Conditions (jointly with Sebastian Bauer, Patrizio Neff and Dirk Pauly), ESAIM: Control, Optimization and Calculus of Variations 22 (2016), 112-133
  • Flächen- und kantenbasierte Finite-Element-Approximationen in der Festkörpermechanik (jointly with Benjamin Müller), GAMM-Rundbrief 1/2016, 4-9
  • First-Order System Least Squares on Curved Boundaries: Higher-Order Raviart-Thomas Elements (jointly with Fleurianne Bertrand and Steffen Münzenmaier), SIAM Journal on Numerical Analysis 52 (2014), 3165-3180
  • A First-Order System Least Squares Method for Hyperelasticity (jointly with Benjamin Müller, Alexander Schwarz and Jörg Schröder), SIAM Journal on Scientific Computing 36 (2014), B795-B816
  • First-Order System Least Squares on Curved Boundaries: Lowest-Order Raviart-Thomas Elements (jointly with Fleurianne Bertrand and Steffen Münzenmaier), SIAM Journal on Numerical Analysis 52 (2014), 880-894
  • New Poincaré-Type Inequalities (jointly with Sebastian Bauer, Patrizio Neff and Dirk Pauly), C. R. Acad. Sci. Paris, Ser. I 352, pp. 163-166 (2014)
  • Efficient Solvers for Mixed Finite Element Discretizations of Nonlinear Problems in Solid Mechanics, in: Modelling, Simulation and Software Concepts for Scientific-Technological Problems (edited by E. Stephan, P. Wriggers), Springer Lecture Notes in Applied and Computational Mechanics 57, pp. 201-209 (2011)
  • Analysis of a Modified First-Order Least Squares Method for Linear Elasticity with Improved Momentum Balance (jointly with Alexander Schwarz and Jörg Schröder), SIAM Journal on Numerical Analysis 49 (2011), 1006-1022
  • First-Order System Least Squares for Coupled Stokes-Darcy Flow (jointly with Steffen Münzenmaier), SIAM Journal on Numerical Analysis 49 (2011), 387-404
  • Adaptive Least Squares Finite Element Methods in Elasto-Plasticity, LSSC 2009 (edited by I. Lirkov, S. Margenov, J. Wasniewski), Springer Lecture Notes in Computer Science 5910, pp. 671-678 (2010)
  • A Modified Least-Squares Mixed Finite Element with Improved Momentum Balance (jointly with Alexander Schwarz and Jörg Schröder), International Journal for Numerical Methods in Engineering 81 (2010), 286-306
  • First-Order System Least Squares for the Signorini Contact Problem in Linear Elasticity (jointly with Frank S. Attia and Zhiqiang Cai), SIAM Journal on Numerical Analysis 47 (2009), 3027-3043
  • Least-Squares Mixed Finite Elements for Small Strain Elasto-Viscoplasticity (jointly with A. Schwarz and J. Schröder), International Journal for Numerical Methods in Engineering 77 (2009), 1351-1370
  • First-Order System Least-Squares for Darcy-Stokes Flow (jointly with Garvin Danisch), SIAM Journal on Numerical Analysis 45 (2007), 731-745
  • An Adaptive Least-Squares Mixed Finite Element Method for Elasto-Plasticity, SIAM Journal on Numerical Analysis 45 (2007), 371-388
  • Finite Element Analysis of Poro-Elastic Consolidation in Porous Media: Standard and Mixed Approaches (jointly with Johannes Korsawe and Olaf Kolditz and Wenqing Wang), Computer Methods in Applied Mechanics and Engineering 195 (2006), 1096-1115
  • On Discrete Korn's Inequality for some Nonconforming Finite Element Approaches to Linear Elasticity (jointly with Frank S. Attia), Proc. Appl. Math. Mech. 5 (2005), 823-824
  • An Adaptive Mixed Finite Element Method for Elasto-Plastic Consolidation (jointly with Jörg Kubitz), Proceedings 5. Workshop ``Porous Media'' (edited by Olaf Kolditz et.al.), University of Tübingen (2005)
  • Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I (jointly with Markus Berndt and Thomas A. Manteuffel and Stephen F. McCormick), SIAM Journal on Numerical Analysis 43 (2005), 386-408
  • A Least-Squares Mixed Finite Element Method for Biot's Consolidation Problem in Porous Media (jointly with Johannes Korsawe), SIAM Journal on Numerical Analysis 43 (2005), 318-339
  • A First-Order System Least-Squares Finite Element Method for the Shallow Water Equations, SIAM Journal on Numerical Analysis 42 (2005), 2387-2407
  • An Adaptive Least Squares Mixed Finite Element Method for the Stress-Displacement Formulation of Linear Elasticity (jointly with Zhiqiang Cai and Johannes Korsawe), Numerical Methods for Partial Differential Equations 21 (2005), 132-148
  • A Preconditioner for the Equations of Linear Elasticity Discretized by the PEERS Element (jointly with Axel Klawonn), Numerical Linear Algebra with Applications 11 (2004), 493-510
  • Least-Squares Methods for Linear Elasticity (jointly with Zhiqiang Cai), SIAM Journal on Numerical Analysis 42 (2004), 826-842
  • Numerical Approximation of Water-Air Two-Phase Flow by the Mixed Finite Element Method (jointly with Johannes Korsawe, Eugen Perau and Susanne Potthoff), Computers and Geotechnics 30 (2003), 695-705
  • A Least Squares Mixed Finite Element Method for Variably Saturated Subsurface Flow in Deformable Porous Media (jointly with Johannes Korsawe), Proceedings 4. Workshop ``Porous Media'' (edited by Olaf Kolditz et.al.), University of Tübingen (2003)
  • First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity (jointly with Zhiqiang Cai), SIAM Journal on Numerical Analysis 41 (2003), 715-730
  • Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms (jointly with Mohammad Majidi), SIAM Journal on Numerical Analysis 39 (2002), 1648-1666
  • Least-Squares Galerkin Methods for Parabolic Problems I: Semi-Discretization in Time (jointly with Mohammad Majidi), SIAM Journal on Numerical Analysis 39 (2001), 1302-1323
  • Gauss-Newton Multilevel Methods for Least-Squares Finite Element Computations of Variably Saturated Subsurface Flow, Computing 64 (2000), 323-338
  • Least-Squares Mixed Finite Element Solution of Variably Saturated Subsurface Flow Problems, SIAM Journal on Scientific Computing 21 (2000), 1869-1885
  • Multilevel Projection Methods for Nonlinear Least-Squares Finite Element Computations (jointly with Johannes Korsawe), Electronic Transactions on Numerical Analysis 10 (2000), 56-73
  • Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films: 1. Calculation for Model Cylindrical and Slit Pores (jointly with Jürgen Adolphs and Nikolai V. Churaev), Journal of Colloid and Interface Science 221 (2000), 246-253
  • A Boundary Functional for the Least-Squares Finite Element Solution of Neutron Transport Problems (jointly with Thomas A. Manteuffel and Klaus J. Ressel), SIAM Journal on Numerical Analysis 37 (2000), 556-586
  • Multilevel Boundary Functionals for Least-Squares Mixed Finite Element Methods, SIAM Journal on Numerical Analysis 36 (1999), 1065-1077
  • Coarse Space Orthogonalization for Indefinite Linear Systems of Equations Arising in Geometrically Nonlinear Elasticity (jointly with Jens Georg Schmidt), Applied Numerical Mathematics 30 (1999), 267-280
  • Block Triangular Preconditioners for Nonsymmetric Saddle Point Problems: Field-of-Values Analysis (jointly with Axel Klawonn), Numerische Mathematik 81 (1999), 577-594
  • Multilevel Methods using Exponential Test Functions on Triangles for Convection-Diffusion Problems , Iterative Methods in Scientific Computation (edited by J. Wang, M. B. Allen III, B. M. Chen, T. Mathew), IMACS Series in Computational and Applied Mathematics 4, pages 185-190 (1998)
  • Multilevel Computation of Streamline Diffusion Finite Element Discretizations for Convection-Diffusion Problems, Large-Scale Scientific Computations of Engineering and Environmental Problems (edited by M. Griebel, O. P. Iliev, S. D. Margenov, P. S. Vassilevski), Notes on Numerical Fluid Mechanics 62, pages 281-289, Vieweg-Verlag (1998)
  • Multilevel Preconditioning Based on Discrete Symmetrization for Convection-Diffusion Equations (jointly with Michael Griebel), Journal of Computational and Applied Mathematics 83 (1997), 165-183
  • Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems, Numerische Mathematik 78 (1997), 103-117
  • Subspace orthogonalization for substructuring preconditioners for nonselfadjoint elliptic problems, SIAM Journal on Scientific Computing 18 (1997), 1108-1121
  • Multilevel minimal residual methods for nonsymmetric elliptic problems, Numerical Linear Algebra with Applications 3 (1996), 351-367
  • First-order system least squares for second-order elliptic problems with discontinuous coefficients (jointly with Thomas A. Manteuffel und Stephen F. McCormick), Proceedings of the 7th Copper Mountain Conference on Multigrid Methods, NASA (1996), 535-550
  • Multilevel preconditioning for the time-harmonic Maxwell equations, 12th Annual Review of Progress in Applied Computational Electromagnetics, (1996), 630-637
  • On hybrid iterative methods for nonsymmetric systems of linear equations (jointly with Thomas A. Manteuffel), Numerische Mathematik 73 (1996), 489-506
  • Preconditioned Krylov subspace methods for Lyapunov matrix equations (jointly with Marlis Hochbruck), SIAM Journal on Matrix Analysis and Applications 16 (1995), 156-171
  • Adaptive k-step iterative methods for nonsymmetric systems of linear equations (jointly with Thomas A. Manteuffel and Richard S. Varga), Electronic Transactions on Numerical Analysis 3 (1995), 50-65
  • Alternating direction preconditioning for nonsymmetric systems of linear equations, SIAM Journal on Scientific Computing 15 (1994), 369--384
  • On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems (jointly with Howard C. Elman and Gene H. Golub), Numerische Mathematik 67 (1994), 177-190
  • Hybrid iterative methods based on Faber polynomials, Linear Algebra for Large Scale and Real-Time Applications (1993), 421-422
  • A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations (jointly with Richard S. Varga), Numerische Mathematik 64 (1993), 213-240
  • Fields of values and the ADI method for non-normal matrices, Linear Algebra and Applications 180 (1993), 199-218
  • Fejer-Walsh points for rational functions and their use in the ADI iterative method, Journal of Computational and Applied Mathematics 46 (1993), 129-141
  • SOR-like Methods for Lyapunov Matrix Equations, Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, North-Holland (1992), 233-240
  • Near-circularity for the rational Zolotarev problem in the complex plane, Journal of Approximation Theory 70 (1992), 115-130
  • Optimal ADI parameters for nonsymmetric systems of linear equations, SIAM Journal on Numerical Analysis 28 (1991), 1431-1445
  • SOR for AX - XB = C (jointly with Wilhelm Niethammer), Linear Algebra and Applications 154-156 (1991), 355-375
  • The near-best solution of a polynomial minimization problem by the Carathéodory-Fejér method (jointly with Michael Eiermann), Constructive Approximation 6 (1990) 303-319
  • Untersuchungen eines Iterationsverfahrens zur Lösung der Lyapunov-Matrix-Gleichung, ZAMM 69 (1989), T193-T195