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Volume 6, Issue 2
$L^2$ Norm Equivalent a Posteriori Error Estimate for a Constrained Optimal Control Problem

L. Ge, W. Liu & D. Yang

Int. J. Numer. Anal. Mod., 6 (2009), pp. 335-353.

Published online: 2009-06

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  • Abstract

Adaptive finite element approximation for a constrained optimal control problem is studied. A posteriori error estimators equivalent to the $L^2$ norm of the approximation error are derived both for the state and the control approximation, which are particularly suitable for an adaptive multi-mesh finite element scheme and applications where $L^2$ error is more important. The error estimators are then implemented and tested with promising numerical results.

  • Keywords

Convex optimal control problem, adaptive finite element method, $L^2$ norm equivalent a posteriori error estimate, multi-meshes.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-335, author = {L. Ge, W. Liu and D. Yang}, title = {$L^2$ Norm Equivalent a Posteriori Error Estimate for a Constrained Optimal Control Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {2}, pages = {335--353}, abstract = {

Adaptive finite element approximation for a constrained optimal control problem is studied. A posteriori error estimators equivalent to the $L^2$ norm of the approximation error are derived both for the state and the control approximation, which are particularly suitable for an adaptive multi-mesh finite element scheme and applications where $L^2$ error is more important. The error estimators are then implemented and tested with promising numerical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/771.html} }
TY - JOUR T1 - $L^2$ Norm Equivalent a Posteriori Error Estimate for a Constrained Optimal Control Problem AU - L. Ge, W. Liu & D. Yang JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 335 EP - 353 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/771.html KW - Convex optimal control problem, adaptive finite element method, $L^2$ norm equivalent a posteriori error estimate, multi-meshes. AB -

Adaptive finite element approximation for a constrained optimal control problem is studied. A posteriori error estimators equivalent to the $L^2$ norm of the approximation error are derived both for the state and the control approximation, which are particularly suitable for an adaptive multi-mesh finite element scheme and applications where $L^2$ error is more important. The error estimators are then implemented and tested with promising numerical results.

L. Ge, W. Liu and D. Yang. (2009). $L^2$ Norm Equivalent a Posteriori Error Estimate for a Constrained Optimal Control Problem. International Journal of Numerical Analysis and Modeling. 6 (2). 335-353. doi:
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