3 papers
math.NA2020
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…
math.AP2019
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.…
math.NA2019
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…