A discontinuous Galerkin finite element method for Hamilton–Jacobi–Bellman equations on piecewise curved domains, with applications to Monge–Ampère type equations

Seminar series

Numerical Analysis Group Internal Seminar

Date

Tue, 23 Jan 2018

Time

14:00 - 14:30

Location

Speaker

Ellya Kawecki

Organisation

OxPDE

We introduce a discontinuous Galerkin finite element method (DGFEM) for Hamilton–Jacobi–Bellman equations on piecewise curved domains, and prove that the method is consistent, stable, and produces optimal convergence rates. Upon utilising a long standing result due to N. Krylov, we may characterise the Monge–Ampère equation as a HJB equation; in two dimensions, this HJB equation can be characterised further as uniformly elliptic HJB equation, allowing for the application of the DGFEM