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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.

  • Keywords

optimal control, Stokes equations, finite element approximation, global superconvergence, recovery, a posteriori error estimate.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-283, author = {H. Liu and N. Yan}, 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 AU - H. Liu & N. Yan 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 and N. Yan. (2006). 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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