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Volume 5, Issue 5
A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

Xianbing Luo, Yanping Chen & Yunqing Huang

DOI: 10.4208/aamm.12-m1296

Adv. Appl. Math. Mech., 5 (2013), pp. 688-704.

Published online: 2013-05

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  • Abstract

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test the theoretical result.

  • Keywords

Variational discretization, parabolic optimal control problems, finite volume element method, distributed control, Crank-Nicolson.

  • AMS Subject Headings

65M15, 65N08, 49M05, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-688, author = {Luo , XianbingChen , Yanping and Huang , Yunqing}, title = {A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {5}, pages = {688--704}, abstract = {

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test the theoretical result.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1296}, url = {http://global-sci.org/intro/article_detail/aamm/92.html} }
TY - JOUR T1 - A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems AU - Luo , Xianbing AU - Chen , Yanping AU - Huang , Yunqing JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 688 EP - 704 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.12-m1296 UR - https://global-sci.org/intro/article_detail/aamm/92.html KW - Variational discretization, parabolic optimal control problems, finite volume element method, distributed control, Crank-Nicolson. AB -

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test the theoretical result.

Luo , XianbingChen , Yanping and Huang , Yunqing. (2013). A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems. Advances in Applied Mathematics and Mechanics. 5 (5). 688-704. doi:10.4208/aamm.12-m1296
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