Efficient Inversion of the Galerkin Matrix of General Second Order Elliptic Operators with Non-Smooth Coefficients

Mario Bebendorf

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Submission date: 26. Feb. 2004
Pages: 24
published in: Mathematics of computation, 74 (2005) 251, p. 1179-1199 
DOI number (of the published article): 10.1090/S0025-5718-04-01716-8
Bibtex
MSC-Numbers: 35C20, 65F05, 65F50
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Abstract:
This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second order elliptic operators with $L^\infty$-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices ($\mathcal{H}$-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity.