|
Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 2, Pages 185–199
(Mi sjvm509)
|
|
|
|
Superconvergence and a posteriori error estimates of RT1 mixed methods for elliptic control problems with an integral constraint
T. Hou Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, P. R. China
Abstract:
In this paper, we investigate the superconvergence property and a posteriori error estimates of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by order $k=1$ Raviart–Thomas mixed finite element spaces, and the control variable is approximated by piecewise constant functions. Approximations of the optimal control of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order $h^2$. Moreover, we derive a posteriori error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.
Key words:
elliptic equations, optimal control problems, superconvergence, a posteriori error estimates, mixed finite element methods, postprocessing.
Received: 17.10.2011
Citation:
T. Hou, “Superconvergence and a posteriori error estimates of RT1 mixed methods for elliptic control problems with an integral constraint”, Sib. Zh. Vychisl. Mat., 16:2 (2013), 185–199; Num. Anal. Appl., 6:2 (2013), 163–175
Linking options:
https://www.mathnet.ru/eng/sjvm509 https://www.mathnet.ru/eng/sjvm/v16/i2/p185
|
Statistics & downloads: |
Abstract page: | 187 | Full-text PDF : | 65 | References: | 21 | First page: | 5 |
|