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

Författare och institution:
Mohammad Asadzadeh (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Alfred, H. Schatz (-); Wolfgang Wendland (-)
Publicerad i:
Mathematics of Computation, 78 ( 4 ) s. 1951-1973
ISSN:
0025-5718
E-ISSN:
1088-6842
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Sammanfattning (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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Beräkningsmatematik ->
Tillämpad matematik
Nyckelord:
Richardson extrapolation, local estimates, asymptotic error expansion inequalities, similarity of subspaces, scalings, finite element method, elliptic equations
Postens nummer:
103184
Posten skapad:
2009-12-09 14:42
Posten ändrad:
2016-07-13 14:09

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