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**Harvard**

Asadzadeh, M., Schatz, A. och Wendland, W. (2009) *A new approach to Richardson extrapolation in the finite element method for second order elliptic problems*.

** BibTeX **

@article{

Asadzadeh2009,

author={Asadzadeh, Mohammad and Schatz, Alfred, H. and Wendland, Wolfgang},

title={A new approach to Richardson extrapolation in the finite element method for second order elliptic problems},

journal={Mathematics of Computation},

issn={0025-5718},

volume={78},

issue={4},

pages={1951-1973},

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.},

year={2009},

keywords={Richardson extrapolation, local estimates, asymptotic error expansion inequalities, similarity of subspaces, scalings, finite element method, elliptic equations },

}

** RefWorks **

RT Journal Article

SR Print

ID 103184

A1 Asadzadeh, Mohammad

A1 Schatz, Alfred, H.

A1 Wendland, Wolfgang

T1 A new approach to Richardson extrapolation in the finite element method for second order elliptic problems

YR 2009

JF Mathematics of Computation

SN 0025-5718

VO 78

IS 4

SP 1951

OP 1973

AB 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.

LA eng

OL 30