Goal-oriented adaptive finite element method for semilinear elliptic PDEs
Roland Becker, Maximilian Brunner, Michael Innerberger, Jens Markus, Melenk, Dirk Praetorius
TL;DR
This paper develops a goal-oriented adaptive finite element method for semilinear elliptic PDEs, demonstrating linear and optimal algebraic convergence rates through a dual problem linearization approach.
Contribution
It introduces a novel adaptive strategy that linearizes the dual problem within the finite element framework for semilinear elliptic PDEs.
Findings
Proves linear convergence of the method.
Establishes optimal algebraic convergence rates.
Validates the approach for goal-oriented error control.
Abstract
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.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Differential Equations and Numerical Methods · Numerical methods for differential equations