International Journal of Differential Equations

Finite Volume Element Approximation for the Elliptic Equation with Distributed Control

Abstract

In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. The error estimation shows that the combination of variational discretization and finite volume element formulation allows optimal convergence. Numerical results are provided to support our theoretical analysis.

Article information

Source
Int. J. Differ. Equ., Volume 2018, Special Issue (2018), Article ID 4753792, 11 pages.

Dates
Revised: 21 April 2018
Accepted: 3 September 2018
First available in Project Euclid: 14 December 2018

https://projecteuclid.org/euclid.ijde/1544756580

Digital Object Identifier
doi:10.1155/2018/4753792

Mathematical Reviews number (MathSciNet)
MR3875741

Citation

Wang, Quanxiang; Zhao, Tengjin; Zhang, Zhiyue. Finite Volume Element Approximation for the Elliptic Equation with Distributed Control. Int. J. Differ. Equ. 2018, Special Issue (2018), Article ID 4753792, 11 pages. doi:10.1155/2018/4753792. https://projecteuclid.org/euclid.ijde/1544756580

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