A Posteriori Error Estimate for Boundary Control Problems Governed by the Parabolic Partial Differential Equations

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Volume 27, Issue 1

Wei Gong & Ningning Yan

DOI:

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.

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@Article{JCM-27-68, author = {}, 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 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 KW - Finite element method KW - A posteriori error estimate KW - 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 & Ningning Yan. (2019). 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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