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

Bramble, James H.

doi:10.1090/S0025-5718-1995-1308447-2

Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory
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Math. Comp. 64 (1995), 1359-1365 Request permission

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.

References

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On discrete norm estimates related to multilevel preconditioners in the finite element method

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