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An abstract analysis of optimal goal-oriented adaptivity

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

Authors

Michael Feischl dirk.praetorius@tuwien.ac.at

Dirk Praetorius m.feischl@unsw.edu.au



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.

Journal Article Type Article
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
APA6 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
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
Publisher URL http://epubs.siam.org/doi/abs/10.1137/15M1021982
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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