# A multigrid framework applied to an elliptic optimal control problem with reduced regularity

## Dr. Stefan Takacs

**March 20, 2012, 4 p.m. S2 059**

In this talk we consider the convergence theory for all-at-once multigrid methods for solving

saddle point problems, like the optimality system of a PDE-constrained optimization problem. For

general linear systems we identify four sufficient conditions for convergence. The analysis follows

classical lines. The result may be an essential help if a parameter-dependent problem is considered,

because the fact that the four sufficient conditions are satisfied with constants independent of the

parameters implies that also the bounds for the convergence rates are parameter-independent.

We apply this theory to an elliptic optimal control model problem of tracking type. The new

approach allows to extend previously known convergence results based on full elliptic regularity

to problems with reduced regularity.