We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite element solution of a linearized dual problem, where the linearization is part of the adaptive strategy. Linear convergence and optimal algebraic convergence rates are shown.
@article{arxiv.2112.06687,
title = {Goal-oriented adaptive finite element method for semilinear elliptic PDEs},
author = {Roland Becker and Maximilian Brunner and Michael Innerberger and Jens Markus Melenk and Dirk Praetorius},
journal= {arXiv preprint arXiv:2112.06687},
year = {2022}
}