Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems

Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems

Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 55–71

Abstract

Asymptotic error expansions in $H^1$-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectangular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.09-m1001

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 55–71

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Optimal control problem Finite element methods Asymptotic error expansions Defect correction A posteriori error estimates.

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