Graduate Seminar

 

Tuesday Jul 9, 2013, 03.30 pm

A Finite Element Method for Hamilton-Jacobi-Bellman equations

Dr. Max Jensen (University of Sussex)

Abstract:
Hamilton-Jacobi-Bellman equations describe how the cost of an opti-
mal control problem changes as problem parameters vary. This talk will address
how Galerkin methods can be adapted to solve these equations efficiently. In par-
ticular, it is discussed how the convergence argument by Barles and Souganidis
for finite difference schemes can be extended to Galerkin finite element methods
to ensure convergence to viscosity solutions. A key question in this regard is the
formulation of the consistency condition. Due to the Galerkin approach, coercivity
properties of the HJB operator may also be satisfied by the numerical scheme. In
this case one achieves besides uniform also strong H 1 convergence of numerical
solutions on unstructured meshes.

Time: 03:30 pm

Location: Seminargebäude, Room SG 11, Wüllnerstraße 5 b, 52062 Aachen