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Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs.
- Source :
-
Computers & Mathematics with Applications . Jul2022, Vol. 118, p18-35. 18p. - Publication Year :
- 2022
-
Abstract
- We formulate and analyze a goal-oriented adaptive finite element method for a semilinear elliptic PDE and a linear goal functional. The discretization is based on finite elements of arbitrary (but fixed) polynomial degree and involves a linearized dual problem. The linearization is part of the proposed algorithm, which employs a marking strategy different to that of standard adaptive finite element methods. Moreover, unlike the well-known dual-weighted residual strategy, the analyzed error estimators are completely computable. We prove linear convergence and, for the first time in the context of goal-oriented adaptivity for nonlinear PDEs, optimal algebraic convergence rates. In particular, the analysis does not require a sufficiently fine initial mesh. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GOAL (Psychology)
*FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 118
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 157388518
- Full Text :
- https://doi.org/10.1016/j.camwa.2022.05.008