Goal-oriented adaptive finite element method for semilinear elliptic PDEs

2021/12/13 by Roland Becker, Maximilian Brunner, Michael Innerberger +2 · 1 voice
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #math.NA

paper · pdf · doi:10.1016/j.camwa.2022.05.008

arxiv published 2021/12/13 · arxiv updated 2021/12/13 · openalex publication_date 2022/05/24 · openalex created_date 2022/05/25 · openalex updated_date 2026/08/01

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.

Discussions

• AUTOMATIC REPOST OF OLD TWEETS FROM TWITTER (X) FOR ARCHIVING PURPOSES [14.12.2021] --- New preprint on "Goal-oriented adaptive finite element method for semilinear elliptic PDEs" by R. Becker, M. Bru [bsky, 0 points, 0 comments]

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