2020/03/31 by Roland Becker, Michael Innerberger, Dirk Praetorius · 1 citation
Mathematics · Computer Science · #math.NA #cs.NA
paper · pdf · doi:10.1515/cmam-2020-0044
published as Computational Methods in Applied Mathematics (2021)
arxiv created 2020/10/09 · arxiv updated 2021/02/18
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.