## Dmitriy Leykekhman (University of Connecticut)-Parabolic optimal control problems with point controls

Mathematics - Colloquium

Friday, March 29, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: In the talk I will consider the optimal control constrained by partial differential equations (PDEs). In the first part of the talk I will review basic theory of the PDE constrained optimization problems for simple model problem. I will show that the problem is well posed and can well be approximated numerically. In the second part of the talk I will consider a specific parabolic optimal control problem with a point controls in space, but variable in time, in two space dimensions. This problem is challenging due to low regularity of the state equation. The standard continuous piece-wise linear approximation in space and the first order discontinuous Galerkin method in time are used to approximate the problem numerically. Despite low regularity we obtain almost optimal h^2+k convergence rate for the control. The main ingredients of the analysis are sharp regularity results and the new global and local fully discrete a priori pointwise in space and L^2 in time error estimates the parabolic problems.

Suggested Audiences:
Adult, College

E-mail:
ma-chair@wpi.edu

Last Modified: March 4, 2013 at 10:11 AM

## Dmitriy Leykekhman (University of Connecticut)-Parabolic optimal control problems with point controls

Mathematics - Colloquium

Friday, March 29, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: In the talk I will consider the optimal control constrained by partial differential equations (PDEs). In the first part of the talk I will review basic theory of the PDE constrained optimization problems for simple model problem. I will show that the problem is well posed and can well be approximated numerically. In the second part of the talk I will consider a specific parabolic optimal control problem with a point controls in space, but variable in time, in two space dimensions. This problem is challenging due to low regularity of the state equation. The standard continuous piece-wise linear approximation in space and the first order discontinuous Galerkin method in time are used to approximate the problem numerically. Despite low regularity we obtain almost optimal h^2+k convergence rate for the control. The main ingredients of the analysis are sharp regularity results and the new global and local fully discrete a priori pointwise in space and L^2 in time error estimates the parabolic problems.

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: March 4, 2013 at 10:11 AM