4 papers · 1 filter
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…
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…
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…