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

Y. Yanping Che & Yuelong Tang

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 ǫ is small enough, while multiscale finite element method is useful for any parameter ǫ.

  • Keywords

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

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@Article{EAJAM-1-235, author = {Y. Yanping Che and Yuelong Tang}, 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 ǫ is small enough, while multiscale finite element method is useful for any parameter ǫ.

}, 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 - Y. Yanping Che & Yuelong Tang 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 KW - finite element method KW - multiscale finite element method KW - homogenization KW - 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 ǫ is small enough, while multiscale finite element method is useful for any parameter ǫ.

Y. Yanping Che & Yuelong Tang. (1970). 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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