Abstract
In this paper, we study the mixed finite element methods for general convex optimal control problems governed by integro-differential equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is discretized by piecewise constant elements. We derive a posteriori error estimates for the coupled state and control approximation. Such estimates are obtained for some model problems which frequently appear in many applications. MSC: 49J20; 65N30
Highlights
1 Introduction The finite element discretization of optimal control problems has been extensively investigated in early literature
In [ ], the authors derived a posteriori error estimators for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach
Brunner and Yan [ ] discussed finite element Galerkin discretization of a class of constrained optimal control problems governed by integral equations and integro-differential equations
Summary
The finite element discretization of optimal control problems has been extensively investigated in early literature. In [ ], the authors derived a posteriori error estimators for a class of distributed elliptic optimal control problems. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach.
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