Convergence Rates of AFEM with H −1 Data

Albert Cohen, Ronald DeVore, Ricardo H. Nochetto

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

This paper studies adaptive finite element methods (AFEMs), based on piecewise linear elements and newest vertex bisection, for solving second order elliptic equations with piecewise constant coefficients on a polygonal domain Ω⊂ℝ2. The main contribution is to build algorithms that hold for a general right-hand side f∈H-1(Ω). Prior work assumes almost exclusively that f∈L2(Ω). New data indicators based on local H-1 norms are introduced, and then the AFEMs are based on a standard bulk chasing strategy (or Dörfler marking) combined with a procedure that adapts the mesh to reduce these new indicators. An analysis of our AFEM is given which establishes a contraction property and optimal convergence rates N-s with 0
Original languageEnglish (US)
Pages (from-to)671-718
Number of pages48
JournalFoundations of Computational Mathematics
Volume12
Issue number5
DOIs
StatePublished - Jun 29 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This research was supported by the Office of Naval Research Contracts ONR-N00014-08-1-1113, ONR N00014-09-1-0107; the AFOSR Contract FA95500910500; the ARO/DoD Contract W911NF-07-1-0185; the NSF Grants DMS-0915231, DMS-0807811, and DMS-1109325; the Agence Nationale de la Recherche (ANR) project ECHANGE (ANR-08-EMER-006); the excellence chair of the Fondation "Sciences Mathematiques de Paris" held by Ronald DeVore. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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