Volume 3, Issue 3
Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

East Asian J. Appl. Math., 3 (2013), pp. 209-227.

Published online: 2018-02

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• Abstract

In this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the $L^2$ projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

• Keywords

Superconvergence, finite element methods, optimal control problems, parabolic equations, interpolation operator.

35B37, 49J20, 65N30

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@Article{EAJAM-3-209, author = {}, title = {Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {3}, pages = {209--227}, abstract = {

In this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the $L^2$ projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030713.100813a}, url = {http://global-sci.org/intro/article_detail/eajam/10919.html} }
TY - JOUR T1 - Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients JO - East Asian Journal on Applied Mathematics VL - 3 SP - 209 EP - 227 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.030713.100813a UR - https://global-sci.org/intro/article_detail/eajam/10919.html KW - Superconvergence, finite element methods, optimal control problems, parabolic equations, interpolation operator. AB -

In this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the $L^2$ projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

Yuelong Tang & Yanping Chen. (1970). Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients. East Asian Journal on Applied Mathematics. 3 (3). 209-227. doi:10.4208/eajam.030713.100813a
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