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

Mohammad Asadzadeh (Institutionen för matematiska vetenskaper, matematik) ; Alfred, H. Schatz ; Wolfgang Wendland
Mathematics of Computation (0025-5718). Vol. 78 (2009), 4, p. 1951-1973.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Richardson extrapolation, local estimates, asymptotic error expansion inequalities, similarity of subspaces, scalings, finite element method, elliptic equations



Denna post skapades 2009-12-09. Senast ändrad 2016-07-13.
CPL Pubid: 103184

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Tillämpad matematik

Chalmers infrastruktur