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.
Highlights
In recent years, the optimization with partial differential equation constraints (PDEs) has received a significant impulse
Priori error estimates for finite element discretization of optimal control problems governed by elliptic equations are discussed in many publications
In [1], a new approach to error control and mesh adaptivity is described for the discretization of the optimal control problems governed by elliptic partial differential equations
Summary
The optimization with partial differential equation constraints (PDEs) has received a significant impulse. Priori error estimates for finite element discretization of optimal control problems governed by elliptic equations are discussed in many publications. In [1], a new approach to error control and mesh adaptivity is described for the discretization of the optimal control problems governed by elliptic partial differential equations. In [4], a priori error analysis for the finite element discretization of the optimal control problems governed by elliptic state equations is considered. In [13], the authors discussed distributed optimal control problems governed by elliptic equations by using the finite volume element methods. In [14], the authors considered the convergence analysis of discontinuous finite volume methods applied to distributed optimal control problems governed by a class of second-order linear elliptic equations.
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