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.

Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

“…So it has been extensively used in computational fluid dynamics. We can refer to [11] for groundwater flow, [12] for weather prediction, [13] for shallow water wave, and to [14] for sedimentation problem. However, there are only a few published results on the finite volume element method for the distributed optimal control problems.…”