Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A new approach to Richardson extrapolation in the finite element method for second order elliptic problems

Authors: M. Asadzadeh, A. H. Schatz and W. Wendland
Journal: Math. Comp. 78 (2009), 1951-1973
MSC (2000): Primary 65N15, 65N30, 35J25
Published electronically: February 11, 2009
MathSciNet review: 2521274
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in $ \mathbb{R}^N$, $ N \ge 2$. The main feature of the approach is that it does not rely on a traditional asymptotic error expansion, but rather depends on a more easily proved weaker a priori estimate, derived in [19], called an asymptotic error expansion inequality. In order to use this inequality to verify that the Richardson procedure works at a point, we require a local condition which links the different subspaces used for extrapolation. Roughly speaking, this condition says that the subspaces are similar about a point, i.e., any one of them can be made to locally coincide with another by a simple scaling of the independent variable about that point. Examples of finite element subspaces that occur in practice and satisfy this condition are given.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65N15, 65N30, 35J25

Retrieve articles in all journals with MSC (2000): 65N15, 65N30, 35J25

Additional Information

M. Asadzadeh
Affiliation: Department of Mathematics, Chalmers University of Technology, SE-412 96 Goteborg, Sweden
Address at time of publication: Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, New York 14853

A. H. Schatz
Affiliation: Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, New York 14853

W. Wendland
Affiliation: Institute for Applied Analysis and Numerical Simulations, University of Stuttgart, Pfaffenwaldring 57, D-750550, Germany

Keywords: Richardson extrapolation, local estimates, asymptotic error expansion inequalities, similarity of subspaces, scalings, finite element method, elliptic equations
Received by editor(s): November 21, 2007
Received by editor(s) in revised form: October 11, 2008
Published electronically: February 11, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.