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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Online
ISSN
1609-9389
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Volume 11, Issue 2 (Jan 2011)

Issues

Layer-adapted methods for a singularly perturbed singular problem

Christian Grossmann
  • nst. fur Numerische Mathematik, Technische Universitat Dresden, Mommsenstr. 13, 01062 Dresden, Germany.
  • Email:
Lars Ludwig
  • Email:
Hans-Görg Roos
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Abstract

In the present paper we analyze linear finite elements on a layer adapted mesh for a boundary value problem characterized by the overlapping of a boundary layer with a singularity. Moreover, we compare this approach numerically with the use of adapted basis functions, in our case modified Bessel functions. It turns out that as well adapted meshes as adapted basis functions are suitable where for our one-dimensional problem adapted bases work slightly better.

Keywords: singularly perturbed boundary value problem; finite elements; layer-adapted mesh; adapted basis functions

About the article

Received: 2010-12-19

Revised: 2011-03-16

Accepted: 2011-05-21

Published in Print:


Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0010. Export Citation

© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY-NC-ND 4.0)

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