Optimal convergence rates for goal-oriented FEM with quadratic goal functional
Numerical Analysis
2021-02-18 v2 Numerical Analysis
Abstract
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 functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [Feischl et al, SIAM J. Numer. Anal., 54 (2016)] for a linear goal functional is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear convergence with optimal convergence rates.
Keywords
Cite
@article{arxiv.2003.13270,
title = {Optimal convergence rates for goal-oriented FEM with quadratic goal functional},
author = {Roland Becker and Michael Innerberger and Dirk Praetorius},
journal= {arXiv preprint arXiv:2003.13270},
year = {2021}
}