Contributions to Books:
R. Becker, M. Innerberger, D. Praetorius:
"Optimal convergence rates for goal-oriented FEM with quadratic goal functional";
in: "ASC Report 7/2020",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
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.
Adaptivity, goal-oriented algorithm, nonlinear quantity of interest, convergence, optimal convergence rates, finite element method.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.