Séminaire du CERAMATHS - DMATHS : exposé de Thomas Apel

Le séminaire du département de mathématiques du CERAMATHS accueillera à 14h Thomas Apel (Universität der Bundeswehr München), jeudi 6 juillet 2023 pour l'exposé suivant :

Finite element solution of optimal control problems with elliptic partial differential equations

Optimal control of partial differential equations (pdes) means the determination of data (called control variable) such that the solution of the pde (called state equation) is optimal in some sense, here as close as possible to a given desired solution. The first order optimality condition is characterized by a system consisting of the state equation, an adjoint equation and an optimality condition.

The problem is then discretized by a finite element method where one has also a choice among different variants. The main contribution of the author and his coauthors of the last 15 years is the estimation of the discretization error in different norms. The basis is always a careful analysis of the regularity of the solution in dependence of the angles of the domain. The convergence order is reduced in the presence of corner and edge singularities. Locally refined finite element meshes are suited to recover the optimal convergence order.