An abstract analysis of optimal goal-oriented adaptivity

Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer George

Abstract

We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, Comput. Math. Appl., 67 (2014), pp. 1195–1253). We prove that this framework covers standard discretizations of general second-order linear elliptic PDEs and hence generalizes available results beyond the Poisson equation.

Citation

Feischl, M., Praetorius, D., & van der Zee, K. G. (in press). An abstract analysis of optimal goal-oriented adaptivity. SIAM Journal on Numerical Analysis, 54(3), https://doi.org/10.1137/15M1021982

• Journal Article Type: Article
• Acceptance Date: Mar 4, 2016
• Online Publication Date: May 12, 2016
• Deposit Date: Apr 7, 2016
• Publicly Available Date: May 12, 2016
• Journal: SIAM Journal on Numerical Analysis
• Print ISSN: 0036-1429
• Electronic ISSN: 1095-7170
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 54
• Issue: 3
• DOI: https://doi.org/10.1137/15M1021982
• Keywords: Adaptivity, goal-oriented algorithm, quantity of interest, convergence, optimal convergence rates, finite element method, boundary element method
• Public URL: https://nottingham-repository.worktribe.com/output/790172
• Publisher URL: http://epubs.siam.org/doi/abs/10.1137/15M1021982
• Additional Information: First published in SIAM Journal on Numerical Analysis in Vol. 54, no. 3, published by the Society for Industrial and Applied Mathematics (SIAM) c2016 Society for Industrial and Applied Mathematics