Zobrazeno 1 - 10
of 186
pro vyhledávání: '"WIHLER, THOMAS P."'
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 polygon $\Omega\subset\mathbb{R}^2$ with a finite number of straight edge
Externí odkaz:
http://arxiv.org/abs/2404.18569
We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy for the redu
Externí odkaz:
http://arxiv.org/abs/2311.13255
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More specifically,
Externí odkaz:
http://arxiv.org/abs/2202.07398
Autor:
Wihler, Thomas P.
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. The purpose of the present paper is to shed new light on Sassenfeld's
Externí odkaz:
http://arxiv.org/abs/2201.05628
Autor:
Metcalfe, Stephen, Wihler, Thomas P.
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 the solution to blow up in finite time. The fully discrete scheme consis
Externí odkaz:
http://arxiv.org/abs/2105.03463
Autor:
Heid, Pascal, Wihler, Thomas P.
The classical Ka\v{c}anov 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 linear problem in each step. Based on this observation, we introd
Externí odkaz:
http://arxiv.org/abs/2101.10137
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. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy contraction prop
Externí odkaz:
http://arxiv.org/abs/2007.10750
Autor:
Heid, Pascal, Wihler, Thomas P.
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 saddle points, rather than being maxima or minima, then the theoretical
Externí odkaz:
http://arxiv.org/abs/2002.06915
Autor:
Wihler, Thomas P., Wirz, Marcel
We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities, anisotropic
Externí odkaz:
http://arxiv.org/abs/1908.04647
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 consists of a combination of gradient flow iterations and adaptive fini
Externí odkaz:
http://arxiv.org/abs/1906.06954