40 citations · 59 across the 24 of their papers we have counts for
35 papers
Iterative finite element approximation of non-monotone semilinear diffusion-reaction equations
Florian Spicher, Thomas P. Wihler
We study iterative linearized finite element methods for the numerical approximation of semilinear elliptic boundary value problems with nonlinear reaction terms of asymptotically…
Weakly convergent fixed point iterations for weakly sequentially non-expansive mappings
Thomas P. Wihler
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often es…
A fully iterative adaptive energy-based approach for monotone elliptic problems
Raphael Leu, Thomas P. Wihler
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first presen…
Iterative energy reduction Galerkin methods and variational adaptivity
Pascal Heid, Thomas P. Wihler
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffu…
Optimal finite element approximations of monotone semilinear elliptic PDE with subcritical nonlinearities
Florian Spicher, Thomas P. Wihler
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical gro…
Gradient Flow Finite Element Discretisations with Energy-Based -Adaptivity for the Gross-Pitaevskii Equation with Angular Momentum
Pascal Heid, Paul Houston, Benjamin Stamm +1
This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects…
Exponential Convergence of -ILGFEM for semilinear elliptic boundary value problems with monomial reaction
Yanchen He, Paul Houston, Christoph Schwab +1
We study the fully explicit numerical approximation of a semilinear elliptic boundary value model problem, which features a monomial reaction and analytic forcing, in a bounded pol…
An -adaptive strategy based on locally predicted error reductions
Patrick Bammer, Andreas Schröder, Thomas P. Wihler
We introduce a new -adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approa…
A numerical energy minimisation approach for semilinear diffusion-reaction boundary value problems based on steady state iterations
Mario Amrein, Pascal Heid, Thomas P. Wihler
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational sch…
A note on the Sassenfeld criterion and its relation to H-matrices
Thomas P. Wihler
The starting point of this note is a decades-old yet little-noticed sufficient condition, presented by Sassenfeld in 1951, for the convergence of the classical Gauss-Seidel method.…
Conditional a posteriori error bounds for high order DG time stepping approximations of semilinear heat models with blow-up
Stephen Metcalfe, Thomas P. Wihler
This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause th…
A modified Kačanov iteration scheme with application to quasilinear diffusion models
Pascal Heid, Thomas P. Wihler
The classical Kačanov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a…
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
Pascal Heid, Dirk Praetorius, Thomas P. Wihler
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Co…
Adaptive local minimax Galerkin methods for variational problems
Pascal Heid, Thomas P. Wihler
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are s…
Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes
Thomas P. Wihler, Marcel Wirz
We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lamé system of linear elasticity in polyhedral domains in . In order to resolv…
Gradient Flow Finite Element Discretizations with Energy-Based Adaptivity for the Gross-Pitaevskii Equation
Pascal Heid, Benjamin Stamm, Thomas P. Wihler
We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and c…
On the Convergence of Adaptive Iterative Linearized Galerkin Methods
Pascal Heid, Thomas P. Wihler
A wide variety of different (fixed-point) iterative methods for the solution of nonlinear equations exists. In this work we will revisit a unified iteration scheme in Hilbert space…
Adaptive Iterative Linearization Galerkin Methods for Nonlinear Problems
Pascal Heid, Thomas P. Wihler
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative lo…
Rounding the arithmetic mean value of the square roots of the first integers
Thomas P. Wihler
In this article we study the arithmetic mean value of the square roots of the first integers. For this quantity, we develop an asymptotic expression, and derive a formul…
The variable-order discontinuous Galerkin time stepping scheme for parabolic evolution problems is uniformly -stable
Lars Schmutz, Thomas P. Wihler
In this paper we investigate the -stability of fully discrete approximations of abstract linear parabolic partial differential equations. The method under consid…
A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems
Emmanuil H. Georgoulis, Omar Lakkis, Thomas P. Wihler
We consider fully discrete time-space approximations of abstract linear parabolic partial differential equations (PDEs) consisting of an -version discontinuous Galerkin (DG) ti…
A Nitsche Finite Element Approach for Elliptic Problems with Discontinuous Dirichlet Boundary Conditions
Ramona Baumann, Thomas P. Wihler
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be r…
-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
Irene Kyza, Stephen Metcalfe, Thomas Wihler
This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existe…
An -Adaptive Newton-Discontinuous-Galerkin Finite Element Approach for Semilinear Elliptic Boundary Value Problems
Paul Houston, Thomas P. Wihler
In this paper we develop an -adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbat…