6 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…
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…
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…