76 citations · 1.5k across the 82 of their papers we have counts for
87 papers
BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions
Michele Aldé, Michael Feischl, Dirk Praetorius
We consider the Landau-Lifshitz-Gilbert equation (LLG) that models time-dependent micromagnetic phenomena. We propose a full discretization that employs first-order finite elements…
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs
Maximilian Brunner, Pascal Heid, Michael Innerberger +3
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with ar…
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite…
-robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs
Michael Innerberger, Ani Miraçi, Dirk Praetorius +1
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric s…
Plain convergence of goal-oriented adaptive FEM
Valentin Helml, Michael Innerberger, Dirk Praetorius
We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general markin…
Goal-oriented adaptivity for multilevel stochastic Galerkin FEM with nonlinear goal functionals
Alex Bespalov, Dirk Praetorius, Michele Ruggeri
This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key n…