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Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory


Author: James H. Bramble
Journal: Math. Comp. 64 (1995), 1359-1365
MSC: Primary 46E35; Secondary 46M35, 65N30
DOI: https://doi.org/10.1090/S0025-5718-1995-1308447-2
MathSciNet review: 1308447
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Abstract: In this paper we describe an interpolation result for the Sobolev spaces $ H_0^s(\Omega )$ where $ \Omega $ is a bounded domain with a Lipschitz boundary. This result is applied to derive discrete norm estimates related to multilevel preconditioners and multigrid methods in the finite element method. The estimates are valid for operators of order 2m with Dirichlet boundary conditions.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1995-1308447-2
Article copyright: © Copyright 1995 American Mathematical Society

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