A priori estimates for optimal Dirichlet boundary control problems

Optimal a priori estimates for interface problems

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...

A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to cons...

A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems

In this article we summarize recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems. We consider the following three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time. For all cases, error estimates with respect...