Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations

Pointwise localized error estimates for parabolic finite element equations

Optimal A Priori Error Estimates of Parabolic Optimal Control Problems with Pointwise Control

In this paper we consider a parabolic optimal control problem with a pointwise (Dirac type) control in space, but variable in time, in two space dimensions. To approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous Galerkin method in time. Despite low regularity of the state equation, we show almost optimal h2 + k ...

A Priori Error Estimates for Three Dimensional Parabolic Optimal Control Problems with Pointwise Control

In this paper we provide an a priori error analysis for parabolic optimal control problems with a pointwise (Dirac type) control in space on three dimensional domains. The two dimensional case was treated in [30], however the three dimensional case is technically much more involved. To approximate the problem we use standard continuous piecewise linear elements in space and piecewise constant d...

Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of themixed finite element solutions for optimal control problems. Such a posteriori ...

Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints

In this paper we consider a model elliptic optimal control problem with finitely many state constraints in two and three dimensions. Such problems are challenging due to low regularity of the adjoint variable. For the discretization of the problem we consider continuous linear elements on quasi-uniform and graded meshes separately. Our main result establishes optimal a priori error estimates fo...