Regularity estimates for elliptic boundary value problems in Besov spaces

Constantin Bacuta; James H. Bramble; Jinchao Xu

doi:10.1090/S0025-5718-02-01502-8

Regularity estimates for elliptic boundary value problems in Besov spaces

Constantin Bacuta, James H. Bramble, Jinchao Xu

Research output: Contribution to journal › Article › peer-review

36 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 language	English (US)
Pages (from-to)	1577-1595
Number of pages	19
Journal	Mathematics of Computation
Volume	72
Issue number	244
DOIs	https://doi.org/10.1090/S0025-5718-02-01502-8
State	Published - Oct 1 2003
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-02-01502-8

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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.",

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N2 - 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.

AB - 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.

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Regularity estimates for elliptic boundary value problems in Besov spaces

Abstract

ASJC Scopus subject areas

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