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Volume 3, Issue 3
Global Superconvergence for Optimal Control Problems Governed by Stokes Equations

H. Liu & N. Yan

Int. J. Numer. Anal. Mod., 3 (2006), pp. 283-302.

Published online: 2006-03

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  • Abstract

In this paper, the global superconvergence analysis for the finite element approximation of the distributed optimal control governed by Stokes equations is discussed. For the control, a global superconvergence result is derived by applying patch recovery technique. For the state and the co-state, the global superconvergence results are derived by applying some postprocessing techniques for the bilinear-constant scheme over the uniform rectangular meshes. Based on the global superconvergence analysis, recovery type a posteriori error estimates are derived. It is shown that the recovery type a posteriori error estimators provided in this paper are asymptotically exact if the conditions for the superconvergence are satisfied.

  • AMS Subject Headings

49J20, 65N30

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-283, author = {}, title = {Global Superconvergence for Optimal Control Problems Governed by Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {3}, pages = {283--302}, abstract = {

In this paper, the global superconvergence analysis for the finite element approximation of the distributed optimal control governed by Stokes equations is discussed. For the control, a global superconvergence result is derived by applying patch recovery technique. For the state and the co-state, the global superconvergence results are derived by applying some postprocessing techniques for the bilinear-constant scheme over the uniform rectangular meshes. Based on the global superconvergence analysis, recovery type a posteriori error estimates are derived. It is shown that the recovery type a posteriori error estimators provided in this paper are asymptotically exact if the conditions for the superconvergence are satisfied.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/901.html} }
TY - JOUR T1 - Global Superconvergence for Optimal Control Problems Governed by Stokes Equations JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 283 EP - 302 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/901.html KW - optimal control, Stokes equations, finite element approximation, global superconvergence, recovery, a posteriori error estimate. AB -

In this paper, the global superconvergence analysis for the finite element approximation of the distributed optimal control governed by Stokes equations is discussed. For the control, a global superconvergence result is derived by applying patch recovery technique. For the state and the co-state, the global superconvergence results are derived by applying some postprocessing techniques for the bilinear-constant scheme over the uniform rectangular meshes. Based on the global superconvergence analysis, recovery type a posteriori error estimates are derived. It is shown that the recovery type a posteriori error estimators provided in this paper are asymptotically exact if the conditions for the superconvergence are satisfied.

H. Liu & N. Yan. (1970). Global Superconvergence for Optimal Control Problems Governed by Stokes Equations. International Journal of Numerical Analysis and Modeling. 3 (3). 283-302. doi:
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