Regularity estimates for elliptic boundary value problems in Besov spaces

Constantin Bacuta, James H. Bramble, Jinchao Xu

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

We consider the Dirichlet problem for Poisson's equation on a nonconvex plane polygonal domain Ω. New regularity estimates for its solution in terms of Besov and Sobolev norms of fractional order are proved. The analysis is based on new interpolation results and multilevel representations of norms on Sobolev and Besov spaces. The results can be extended to a large class of elliptic boundary value problems. Some new sharp finite element error estimates are deduced.

Original languageEnglish (US)
Pages (from-to)1577-1595
Number of pages19
JournalMathematics of Computation
Volume72
Issue number244
DOIs
StatePublished - Oct 1 2003

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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