4 papers
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…
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…
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…