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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
64/2001

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

Boris N. Khoromskij and Jens Markus Melenk

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.

Received:
Oct 5, 2001
Published:
Oct 5, 2001
MSC Codes:
65N35, 65F10, 35D10
Keywords:
hp-finite element methods, meshes refined towards boundary, direct solvers, schur complement

Related publications

inJournal
2002 Repository Open Access
Jens Markus Melenk and Boris N. Khoromskij

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

In: Computing, 69 (2002) 2, pp. 91-117