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Volume 10, Issue 3
Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems

X. Luo, Y. Chen & Y. Huang

Int. J. Numer. Anal. Mod., 10 (2013), pp. 697-711.

Published online: 2013-10

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  • Abstract

In this paper, finite volume element method is applied to solve the distributed optimal control problems governed by an elliptic equation. We use the method of variational discretization concept to approximate the problems. The optimal order error estimates in $L^2$ and $L^∞$-norm are derived for the state, costate and control variables. The optimal $H^1$ and $W^{1,∞}$-norm error estimates for the state and costate variables are also obtained. Numerical experiments are presented to test the theoretical results.

  • Keywords

finite volume element method, variational discretization, optimal control problems, elliptic equation, distributed control.

  • AMS Subject Headings

65N15, 35Q99, 49M25, 35J15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-697, author = {X. Luo, Y. Chen and Y. Huang}, title = {Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {697--711}, abstract = {

In this paper, finite volume element method is applied to solve the distributed optimal control problems governed by an elliptic equation. We use the method of variational discretization concept to approximate the problems. The optimal order error estimates in $L^2$ and $L^∞$-norm are derived for the state, costate and control variables. The optimal $H^1$ and $W^{1,∞}$-norm error estimates for the state and costate variables are also obtained. Numerical experiments are presented to test the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/590.html} }
TY - JOUR T1 - Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems AU - X. Luo, Y. Chen & Y. Huang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 697 EP - 711 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/590.html KW - finite volume element method, variational discretization, optimal control problems, elliptic equation, distributed control. AB -

In this paper, finite volume element method is applied to solve the distributed optimal control problems governed by an elliptic equation. We use the method of variational discretization concept to approximate the problems. The optimal order error estimates in $L^2$ and $L^∞$-norm are derived for the state, costate and control variables. The optimal $H^1$ and $W^{1,∞}$-norm error estimates for the state and costate variables are also obtained. Numerical experiments are presented to test the theoretical results.

X. Luo, Y. Chen and Y. Huang. (2013). Some Error Estimates of Finite Volume Element Approximation for Elliptic Optimal Control Problems. International Journal of Numerical Analysis and Modeling. 10 (3). 697-711. doi:
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