

Preprint 21/2002
Existence of
-Matrix Approximants to the Inverse FE-Matrix of Elliptic Operators with L∞-Coefficients
Mario Bebendorf and Wolfgang Hackbusch
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Submission date: 28. Feb. 2002
Pages: 19
published in: Numerische Mathematik, 95 (2003) 1, p. 1-28
DOI number (of the published article): 10.1007/s00211-002-0445-6
Bibtex
MSC-Numbers: 35C20, 65F05, 65F50, 65N30
Keywords and phrases: hierarchical matrices, inverse fe-matrix, jumping coefficients, green's function
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Abstract:
This article deals with the existence of blockwise low-rank approximants --
so-called -matrices -- to inverses of FEM matrices in the case
of uniformly elliptic operators with
-coefficients. Unlike
operators arising from boundary element methods for which the
-matrix theory has been extensively developed, the inverses of these
operators do not benefit from the smoothness of the kernel function. However,
it will be shown that the corresponding Green functions can be approximated by
degenerate functions giving rise to the existence of blockwise low-rank
approximants of FEM inverses. Numerical examples confirm the correctness of
our estimates. As a side-product we analyse the
-matrix property
of the inverse of the FE mass matrix.