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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Regularity estimates for elliptic boundary value problems in Besov spaces


Authors: Constantin Bacuta, James H. Bramble and Jinchao Xu
Journal: Math. Comp. 72 (2003), 1577-1595
MSC (2000): Primary 65N30, 46B70, 35J67, 35J05
Published electronically: December 18, 2002
MathSciNet review: 1986794
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Abstract: We consider the Dirichlet problem for Poisson's equation on a nonconvex plane polygonal domain $\Omega$. 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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Additional Information

Constantin Bacuta
Affiliation: Dept. of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: bacuta@math.psu.edu

James H. Bramble
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Email: bramble@math.tamu.edu

Jinchao Xu
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: xu@math.psu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01502-8
PII: S 0025-5718(02)01502-8
Keywords: Interpolation spaces, finite element method, multilevel decomposition, shift theorems, Besov spaces
Received by editor(s): January 26, 2002
Received by editor(s) in revised form: March 25, 2002
Published electronically: December 18, 2002
Additional Notes: The work of the second author was supported in part under NSF Grant No. DMS-9973328.
The work of the third author was supported under NSF Grant No. DMS-0074299.
Article copyright: © Copyright 2002 American Mathematical Society