19 citations · 116 across the 13 of their papers we have counts for
13 papers
Multigoal-oriented adaptive finite element method with convergence rates
Roland Becker, Maximilian Brunner, Paula Hilbert +2
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multip…
Energy minimization for skyrmions on planar thin films
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius +1
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmet…
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…
MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs
Michael Innerberger, Dirk Praetorius
We present an easily accessible, object oriented code (written exclusively in Matlab) for adaptive finite element simulations in 2D. It features various refinement routines for tri…
Goal-oriented adaptive finite element method for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger +2
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite elemen…
Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems
Roland Becker, Michael Innerberger, Dirk Praetorius
We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on thi…
Goal-oriented adaptive finite element methods with optimal computational complexity
Roland Becker, Gregor Gantner, Michael Innerberger +1
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-r…
Optimal convergence rates for goal-oriented FEM with quadratic goal functional
Roland Becker, Michael Innerberger, Dirk Praetorius
We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal fun…
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time.…
Instance-optimal goal-oriented adaptivity
Michael Innerberger, Dirk Praetorius
We consider an adaptive finite element method with arbitrary but fixed polynomial degree , where adaptivity is driven by an edge-based residual error estimator. Based on t…