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Volume 27, Issue 1
A Posteriori Error Estimate for Boundary Control Problems Governed by the Parabolic Partial Differential Equations

Wei Gong & Ningning Yan

J. Comp. Math., 27 (2009), pp. 68-88.

Published online: 2009-02

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  • Abstract

In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.

  • Keywords

Boundary control problems, Finite element method, A posteriori error estimate, Parabolic partial differential equations.

  • AMS Subject Headings

49J20, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-68, author = {Wei Gong and Ningning Yan}, title = {A Posteriori Error Estimate for Boundary Control Problems Governed by the Parabolic Partial Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {1}, pages = {68--88}, abstract = {

In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8560.html} }
TY - JOUR T1 - A Posteriori Error Estimate for Boundary Control Problems Governed by the Parabolic Partial Differential Equations AU - Wei Gong & Ningning Yan JO - Journal of Computational Mathematics VL - 1 SP - 68 EP - 88 PY - 2009 DA - 2009/02 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8560.html KW - Boundary control problems, Finite element method, A posteriori error estimate, Parabolic partial differential equations. AB -

In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.

Wei Gong and Ningning Yan. (2009). A Posteriori Error Estimate for Boundary Control Problems Governed by the Parabolic Partial Differential Equations. Journal of Computational Mathematics. 27 (1). 68-88. doi:
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