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

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

Year:    2013

Author:    Xianbing Luo, Yanping Chen, Yunqing Huang

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-m1296

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 5 : pp. 688–704

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

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

Author Details

Xianbing Luo

Yanping Chen

Yunqing Huang

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