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Volume 8, Issue 1
A Posteriori Error Estimates of $hp$-FEM for Optimal Control Problems

W. Gong, W. Liu & N. Yan

Int. J. Numer. Anal. Mod., 8 (2011), pp. 48-69.

Published online: 2011-08

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  • Abstract

In this paper, we investigate a posteriori error estimates of the $hp$-finite element method for a distributed convex optimal control problem governed by the elliptic partial differential equations. A family of weighted a posteriori error estimators of residual type are formulated. Both reliability and efficiency of the estimators are analyzed.

  • Keywords

$hp$-finite element method, optimal control problem, a posteriori error estimates.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-48, author = {W. Gong, W. Liu and N. Yan}, title = {A Posteriori Error Estimates of $hp$-FEM for Optimal Control Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {1}, pages = {48--69}, abstract = {

In this paper, we investigate a posteriori error estimates of the $hp$-finite element method for a distributed convex optimal control problem governed by the elliptic partial differential equations. A family of weighted a posteriori error estimators of residual type are formulated. Both reliability and efficiency of the estimators are analyzed.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/673.html} }
TY - JOUR T1 - A Posteriori Error Estimates of $hp$-FEM for Optimal Control Problems AU - W. Gong, W. Liu & N. Yan JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 48 EP - 69 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/673.html KW - $hp$-finite element method, optimal control problem, a posteriori error estimates. AB -

In this paper, we investigate a posteriori error estimates of the $hp$-finite element method for a distributed convex optimal control problem governed by the elliptic partial differential equations. A family of weighted a posteriori error estimators of residual type are formulated. Both reliability and efficiency of the estimators are analyzed.

W. Gong, W. Liu and N. Yan. (2011). A Posteriori Error Estimates of $hp$-FEM for Optimal Control Problems. International Journal of Numerical Analysis and Modeling. 8 (1). 48-69. doi:
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