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Publications in Scientific Journals:

R. Becker, M. Innerberger, D. Praetorius:
"Optimal convergence rates for goal-oriented FEM with quadratic goal functional";
accepted for publication in Computational Methods in Applied Mathematics (2020), 1 - 24.



English 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:
Adaptivity, goal-oriented algorithm, nonlinear quantity of interest, convergence, optimal convergence rates, finite element method.


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1515/cmam-2020-0044


Created from the Publication Database of the Vienna University of Technology.