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

Tang Liu, Ningning Yan & Shuhua Zhang

DOI: 10.4208/jcm.2009.09-m1001

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

Published online: 2010-02

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  • 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.  

  • 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.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-55, author = {Tang Liu, Ningning Yan and Shuhua Zhang}, title = {Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {1}, pages = {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.  

}, 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 Problems AU - Tang Liu, Ningning Yan & Shuhua Zhang 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, Finite element methods, Asymptotic error expansions, Defect correction, A posteriori error estimates. AB -

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.  

Tang Liu, Ningning Yan and Shuhua Zhang. (2010). Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems. Journal of Computational Mathematics. 28 (1). 55-71. doi:10.4208/jcm.2009.09-m1001
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