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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
45/2001

Boundary concentrated finite element methods

Boris N. Khoromskij and Jens Markus Melenk

Abstract

A method with optimal (up to logarithmic terms) complexity for solving elliptic problems is proposed. The method relies on interior regularity but the solution may have globally low regularity due to rough boundary data or geometries. Elliptic regularity results, high order approximation results, and an efficient preconditioner are presented.

The method is utilized to realize, with linear-logarithmic complexity, an accurate and data-sparse approximations to the associated elliptic Poincaré-Steklov operators. Further applications include the treatment of exterior boundary value problems and its use in the framework of domain decomposition methods.

Received:
Jul 18, 2001
Published:
Jul 18, 2001
MSC Codes:
65N35, 65F10, 35D10
Keywords:
hp-finite element methods, preconditioning, data-sparse approximation to poincaré-steklov oper, meshes refined toward boundary

Related publications

inJournal
2003 Repository Open Access
Boris N. Khoromskij and Jens Markus Melenk

Boundary concentrated finite element methods

In: SIAM journal on numerical analysis, 41 (2003) 1, pp. 1-36