An efficient direct solver for the boundary concentrated FEM in 2D

Boris N. Khoromskij and Jens Markus Melenk

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Submission date: 05. Oct. 2001
Pages: 25
published in: Computing, 69 (2002) 2, p. 91-117 
DOI number (of the published article): 10.1007/s00607-002-1452-2
Bibtex
MSC-Numbers: 65N35, 65F10, 35D10
Keywords and phrases: hp-finite element methods, meshes refined towards boundary, direct solvers, schur complement
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Abstract:
The boundary concentrated FEM, a variant of the hp-version of the finite element method, is proposed for the numerical treatment of elliptic boundary value problems. It is particularly suited for equations with smooth coefficients and boundary conditions that may have low Sobolev regularity. In the two-dimensional case, it is shown that the Cholesky factorization of the resulting stiffness matrix requires O( N log⁴N) units of storage and can be computed with O( N log⁸N) work. Numerical results confirm theoretical estimates.