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Volume 1, Issue 3
Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients

Yanping Chen & Yuelong Tang

DOI: 10.4208/eajam.071010.250411a

East Asian J. Appl. Math., 1 (2011), pp. 235-247.

Published online: 2018-02

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  • Abstract

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter $\varepsilon$ is small enough, while multiscale finite element method is useful for any parameter $\varepsilon$.

  • Keywords

Optimal control problems, finite element method, multiscale finite element method, homogenization, convergence analysis.

  • AMS Subject Headings

65K05, 65K10, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-235, author = {Chen , Yanping and Tang , Yuelong}, title = {Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {3}, pages = {235--247}, abstract = {

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter $\varepsilon$ is small enough, while multiscale finite element method is useful for any parameter $\varepsilon$.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.071010.250411a}, url = {http://global-sci.org/intro/article_detail/eajam/10906.html} }
TY - JOUR T1 - Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients AU - Chen , Yanping AU - Tang , Yuelong JO - East Asian Journal on Applied Mathematics VL - 3 SP - 235 EP - 247 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.071010.250411a UR - https://global-sci.org/intro/article_detail/eajam/10906.html KW - Optimal control problems, finite element method, multiscale finite element method, homogenization, convergence analysis. AB -

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter $\varepsilon$ is small enough, while multiscale finite element method is useful for any parameter $\varepsilon$.

Chen , Yanping and Tang , Yuelong. (2018). Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients. East Asian Journal on Applied Mathematics. 1 (3). 235-247. doi:10.4208/eajam.071010.250411a
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