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Optimal convergence rates for goal-oriented FEM with quadratic goal functional

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.

preprint2020arXivOpen access
Roland BeckerMichael InnerbergerDirk Praetorius
math.NANumerical Analysis
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Roland BeckerMichael InnerbergerDirk Praetorius

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