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An Efficient Direct Solver for the Boundary Concentrated FEM in 2D

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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 non-smooth boundary conditions. In the two-dimensional case it is shown that the Cholesky factorization of the resulting stiffness matrix requires O(Nlog4 N) units of storage and can be computed with O(Nlog8 N) work, where N denotes the problem size. Numerical results confirm theoretical estimates.

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Authors and Affiliations

  1. Max-Planck-Institute for Mathematics in the Sciences Inselstraße. 22-26, D-04103 Leipzig Germany e-mail: {bokh,melenk}@mis.mpg.de, , , , , , DE

    B. N. Khoromskij & J. M. Melenk

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  1. B. N. Khoromskij
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  2. J. M. Melenk
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Received October 4, 2001; revised August 19, 2002 Published online: October 24, 2002

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Khoromskij, B., Melenk, J. An Efficient Direct Solver for the Boundary Concentrated FEM in 2D. Computing 69, 91–117 (2002). https://doi.org/10.1007/s00607-002-1452-2

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  • DOI: https://doi.org/10.1007/s00607-002-1452-2

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