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Wihler, Thomas P. (2023). A GENERALIZED SASSENFELD CRITERION AND ITS RELATION TO H-MATRICES. Electronic transactions on numerical analysis, 58, pp. 621-628. Kent State University and Johann Radon Institute (RICAM) 10.1553/etna_vol58s621
Amrein, Mario; Heid, Pascal; Wihler, Thomas P. (2023). A Numerical Energy Reduction Approach for Semilinear Diffusion-Reaction Boundary Value Problems Based on Steady-State Iterations. Siam journal on numerical analysis, 61(2), pp. 755-783. Society for Industrial and Applied Mathematics 10.1137/22M1478586
Heid, Pascal; Wihler, Thomas P. (2022). A modified Kačanov iteration scheme with application to quasilinear diffusion models. ESAIM: Mathematical modelling and numerical analysis (ESAIM: M2AN), 56(2), pp. 433-450. EDP Sciences 10.1051/m2an/2022008
Metcalfe, Stephen; Wihler, Thomas P. (2022). Conditional a posteriori error bounds for high order discontinuous Galerkin time stepping approximations of semilinear heat models with blow-up. SIAM Journal on Scientific Computing, 44(3), A1337-A1357. Society for Industrial and Applied Mathematics 10.1137/21M1418964
Heid, Pascal; Stamm, Benjamin; Wihler, Thomas P. (2021). Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation. Journal of computational physics, 436, p. 110165. Elsevier 10.1016/j.jcp.2021.110165
Heid, Pascal; Wihler, Thomas P. (2021). Adaptive local minimax Galerkin methods for variational problems. SIAM Journal on Scientific Computing, 43(2), A1108-A1133. Society for Industrial and Applied Mathematics 10.1137/20M1319863
Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P. (2021). Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Computational methods in applied mathematics, 21(2), pp. 407-422. De Gruyter 10.1515/cmam-2021-0025
Georgoulis, Emmanuil H.; Lakkis, Omar; Wihler, Thomas P. (2021). A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems. Numerische Mathematik, 148(2), pp. 363-386. Springer-Verlag 10.1007/s00211-021-01187-7
Wihler, Thomas P.; Wirz, Marcel (2020). Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes. Journal of scientific computing, 82(2) Springer 10.1007/s10915-020-01153-9
Heid, Pascal; Wihler, Thomas P. (2020). On the convergence of adaptive iterative linearized Galerkin methods. Calcolo, 57(3) Springer 10.1007/s10092-020-00368-4
Heid, Pascal; Wihler, Thomas P. (2020). Adaptive iterative linearization Galerkin methods for nonlinear problems. Mathematics of computation, 89(326), pp. 2707-2734. American Mathematical Society 10.1090/mcom/3545
Schmutz, Lars; Wihler, Thomas (2019). The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly L∞-stable. Siam journal on numerical analysis, 57(1), pp. 293-319. Society for Industrial and Applied Mathematics 10.1137/17M1158835
Houston, Paul; Wihler, Thomas (2018). An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of computation, 87(314), pp. 2641-2674. American Mathematical Society 10.1090/mcom/3308
Holm, Bärbel; Wihler, Thomas (2018). Continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems with application to finite time blow-up. Numerische Mathematik, 138(3), pp. 767-799. Springer 10.1007/s00211-017-0918-2
Kyza, Irene; Metcalfe, Stephen Arthur; Wihler, Thomas (2018). hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems. Journal of scientific computing, 75(1), pp. 111-127. Springer 10.1007/s10915-017-0565-x
Baumann, Ramona; Wihler, Thomas (2018). A Nitsche finite element approach for elliptic problems with discontinuous Dirichlet boundary conditions. Computational methods in applied mathematics, 18(3), pp. 373-381. De Gruyter 10.1515/cmam-2017-0057
Amrein, Mario; Wihler, Thomas (2017). An adaptive space-time Newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations. IMA journal of numerical analysis, 37(4), pp. 2004-2019. Oxford University Press 10.1093/imanum/drw049
Amrein, Mario; Wihler, Thomas (2017). Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations. Numerical methods for partial differential equations, 33(6), pp. 2005-2022. Wiley 10.1002/num.22177
Wihler, Thomas (2017). A note on a norm-preserving continuous Galerkin time stepping scheme. Calcolo, 54(3), pp. 657-667. Springer 10.1007/s10092-016-0203-2
Wihler, Thomas (2017). Animal population social structure models. IMA journal of applied mathematics, 82(3), pp. 548-560. Oxford University Press 10.1093/imamat/hxx002
Baumann, Ramona; Wihler, Thomas (2017). A note on Sassenfeld matrices. Elemente der Mathematik, 72(2), pp. 62-65. European Mathematical Society 10.4171/EM/325
Amrein, Mario; Melenk, Jens Markus; Wihler, Thomas (2017). An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Mathematical methods in the applied sciences, 40(6), pp. 1973-1985. Wiley 10.1002/mma.4113
Congreve, Scott Spencer; Wihler, Thomas (2017). Iterative Galerkin discretizations for strongly monotone problems. Journal of computational and applied mathematics, 311, pp. 457-472. Elsevier 10.1016/j.cam.2016.08.014
Houston, Paul; Wihler, Thomas (2016). Adaptive energy minimisation for hp-finite element methods. Computers and mathematics with applications, 71(4), pp. 977-990. Elsevier 10.1016/j.camwa.2016.01.002
Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas (2015). hp-DGFEM for second-order mixed elliptic problems polyhedra. Mathematics of computation, 85(299), pp. 1051-1083. American Mathematical Society 10.1090/mcom/3062
Amrein, Mario; Wihler, Thomas (2015). Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations. SIAM Journal on Scientific Computing, 37(4), A1637-A1657. Society for Industrial and Applied Mathematics 10.1137/140983537
Stamm, Benjamin; Wihler, Thomas (2015). A total variation discontinuous Galerkin approach for image restoration. International Journal of Numerical Analysis and Modeling, 12(1), pp. 81-93. Edmonton: Institute for Scientific Computing and Information
Wihler, Thomas; Bessire, Bänz; Stefanov, André (2014). Computing the entropy of a large matrix. Journal of physics. A - mathematical and theoretical, 47(24), p. 245201. Institute of Physics Publishing IOP 10.1088/1751-8113/47/24/245201
Amrein, Mario; Wihler, Thomas (2014). An adaptive Newton-method based on a dynamical systems approach. Communications in Nonlinear Science and Numerical Simulation, 19(9), pp. 2958-2973. Elsevier 10.1016/j.cnsns.2014.02.010
Fankhauser, Thomas; Wihler, Thomas; Wirz, Marcel (2014). The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements. Computers and mathematics with applications, 67(4), pp. 854-868. Elsevier 10.1016/j.camwa.2013.05.024
Schötzau, D.; Schwab, Ch.; Wihler, T. P. (2013). hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence. Siam journal on numerical analysis, 51(4), pp. 2005-2035. Society for Industrial and Applied Mathematics 10.1137/090774276
Schötzau, D.; Schwab, Ch.; Wihler, T. P. (2013). hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes. Siam journal on numerical analysis, 51(3), pp. 1610-1633. Society for Industrial and Applied Mathematics 10.1137/090772034
Congreve, Scott; Houston, Paul; Wihler, Thomas P. (2013). Two-Grid hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic PDEs. Journal of scientific computing, 55(2), pp. 471-497. New York, N.Y.: Plenum Press 10.1007/s10915-012-9644-1
Wihler, Thomas; Congreve, Scott Spencer; Süli, E. (2013). Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows. IMA journal of numerical analysis, 33(4), pp. 1386-1415. Oxford University Press 10.1093/imanum/drs046
Houston, Paul; Wihler, Thomas P. (2012). Second-Order Elliptic PDE with Discontinuous Boundary Data. IMA journal of numerical analysis, 32(1), pp. 48-74. Oxford: Oxford University Press 10.1093/imanum/drq032
Houston, Paul; Wihler, Thomas Pascal (2012). Discontinuous Galerkin methods for problems with Dirac delta source. Esaim. Mathematical modelling and numerical analysis / Modélisation mathématique et analyse numérique, 46(6), pp. 1467-1483. Paris: EDP Sciences 10.1051/m2an/2012010
Wihler, Thomas P.; Wirz, Marcel (2012). Mixed hp-Discontinuous Galerkin Fem for linear elasticity and Stokes flow in three dimensions. Mathematical models & methods in applied sciences, 22(08), p. 1250016. Singapore: World Scientific 10.1142/S0218202512500169
Schneebeli, Hans Rudolf; Wihler, Thomas P. (2011). The Newton-Raphson method and adaptive ODE solvers. Fractals, 19(1), pp. 87-99. Singapore: World Scientific 10.1142/s0218348x11005191
Bridgeman, Leila J.; Wihler, Thomas P. (2011). Stability and a posteriori error analysis of discontinuous Galerkin methods for linearized elasticity. Computer methods in applied mechanics and engineering, 200(13-16), pp. 1543-1557. Amsterdam: Elsevier 10.1016/j.cma.2010.10.007
Wihler, Thomas P. (2011). An hp-adaptive strategy based on continuous Sobolev embeddings. Journal of computational and applied mathematics, 235(8), pp. 2731-2739. Antwerp: North-Holland 10.1016/j.cam.2010.11.023
Wihler, Thomas P.; Rivière, Béatrice (2011). Discountinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions. Journal of scientific computing, 46(2), pp. 151-165. New York, N.Y.: Springer US; http://www.springer-ny.com 10.1007/s10915-010-9387-9
Schötzau, Dominik; Wihler, Thomas P. (2010). A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations. Numerische Mathematik, 115(3), pp. 475-509. Berlin: Springer-Verlag 10.1007/s00211-009-0285-8
Stamm, Benjamin; Wihler, Thomas P. (2010). hp-optimal discontinuous Galerkin methods for linear elliptic problems. Mathematics of computation, 79(272), pp. 2117-2133. Providence, R.I.: American Mathematical Society 10.1090/S0025-5718-10-02335-5
Wihler, Thomas P. (2009). On the Hölder Continuity of Matrix Functions for Normal Matrices. Journal of inequalities in pure and applied mathematics JIPAM, 10(4) Melbourne: Victoria Univ. of Technology
Houston, Paul; Wihler, Thomas P (2020). An hp-adaptive iterative linearization discontinuous-Galerkin FEM for quasilinear elliptic boundary value problems. In: Sherwin, Spencer J; Moxey, David; Peiró, Joaquim; Vincent, Peter E; Schwab, Christoph (eds.) Spectral and high order methods for partial differential equations. ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering: Vol. 134 (pp. 407-417). Springer 10.1007/978-3-030-39647-3_32
Houston, Paul; Wihler, Thomas P. (2017). An adaptive variable order quadrature strategy. In: Bittencourt, Marco L.; Dumont, Ney A.; Hesthaven, Jan S. (eds.) Spectral and high order methods for partial differential equations. Lecture Notes in Computational Science and Engineering: Vol. 119 (pp. 533-545). Cham: Springer 10.1007/978-3-319-65870-4_38
Janssen, Bärbel; Wihler, Thomas (2015). Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems. In: Kirby, Robert M.; Berzins, Martin; Hesthaven, Jan S. (eds.) Spectral and High Order Methods for Partial Differential Equations -ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering: Vol. 106 (pp. 103-114). Springer 10.1007/978-3-319-19800-2_7
Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas; Wirz, Marcel (2014). Exponential convergence of hp-DGFEM for elliptic problems in polyhedral domains. In: Azaïez, Mejdi; El Fekih, Henda; Hesthaven, Jan S. (eds.) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering: Vol. 95 (pp. 57-73). Springer 10.1007/978-3-319-01601-6_4
Wihler, Thomas (2012). Mathematik für Naturwissenschaften: Einführung in die Analysis [Textbook] . UTB: Vol. 3635. Stuttgart: Haupt Verlag
Wihler, Thomas (2012). Mathematik für Naturwissenschaften: Einführung in die Lineare Algebra [Textbook] . UTB: Vol. 3636. Stuttgart: Haupt Verlag
Melenk, Jens M.; Wihler, Thomas (2014). A Posteriori Error Analysis of hp-FEM for singularly perturbed problems Cornell University Library
Schötzau, D.; Schwab, C.; Wihler, T. (2009). hp-dGFEM for second-order elliptic problems in polyhedra. I: Stability and quasioptimality on geometric meshes Zürich: Eidgenössische Technische Hochschule ETH
Schötzau, D.; Schwab, C.; Wihler, T. (2009). hp-dGFEM for second-order elliptic problems in polyhedra. II: Exponential convergence Zürich: Eidgenössische Technische Hochschule ETH
Houston, Paul; Wihler, Thomas P. (2009). Second-order elliptic PDE with discontinuous boundary data University of Nottingham
Wihler, Thomas P. (2011). An hp-Adaptive FEM Procedure based on Continuous Sobolev Embeddings. In: Proceedings in Applied Mathematics and Mechanics, 82nd Annual GAMM Scientific Conference, Graz, Austria, 2011, PAMM, Vol. 11, No. 1.
Congreve, S.; Houston, P.; Wihler, T.P. (2011). Two-Grid hp-Version DGFEMs for Strongly Monotone Second-Order Quasilinear Elliptic PDEs. In: Proceedings in Applied Mathematics and Mechanics, 82nd Annual GAMM Scientific Conference, Graz, Austria, PAMM, Vol. 11, No. 1.
