Goal-oriented adaptive finite element method for semilinear elliptic PDEs
arXiv:2112.06687 · doi:10.1016/j.camwa.2022.05.008
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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Cited by in corpus (5)
- Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
- A Posteriori Single- and Multi-Goal Error Control and Adaptivity for Partial Differential Equations
- Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
- Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
- Plain convergence of goal-oriented adaptive FEM