Volume 28, Issue 1
Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problem

Tang Liu, Ningning Yan & Shuhua Zhang

J. Comp. Math., 28 (2010), pp. 55-71.

Published online: 2010-02

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  • Abstract

Asymptotic error expansions in H1-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.  

  • Keywords

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

  • AMS Subject Headings

65R20 65M12 65M60 65N30 76S05 49J20.

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COPYRIGHT: © Global Science Press

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@Article{JCM-28-55, author = {}, title = {Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problem}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {55--71}, abstract = {

Asymptotic error expansions in H1-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.  

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m1001}, url = {http://global-sci.org/intro/article_detail/jcm/8507.html} }
TY - JOUR T1 - Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problem JO - Journal of Computational Mathematics VL - 1 SP - 55 EP - 71 PY - 2010 DA - 2010/02 SN - 28 DO - http://doi.org/10.4208/jcm.2009.09-m1001 UR - https://global-sci.org/intro/article_detail/jcm/8507.html KW - Optimal control problem KW - Finite element methods KW - Asymptotic error expansions KW - Defect correction KW - A posteriori error estimates AB -

Asymptotic error expansions in H1-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.  

Tang Liu, Ningning Yan & Shuhua Zhang. (2019). Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problem. Journal of Computational Mathematics. 28 (1). 55-71. doi:10.4208/jcm.2009.09-m1001
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