Mixed Finite Element Methods for Hamilton-Jacobi-Bellman Type Equations

Hamilton-Jacobi-Bellman Equations

This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...

The finite element approximation of Hamilton-Jacobi-Bellman equations: the noncoercive case

This paper deals with the finite element approximation of Hamilton-Jacobi-Bellman equations. We establish a convergence and a quasi-optimal Lm -error estimate, involving a weakly coupled system of quasi-variational inequalities for the solution of which an iterative scheme of monotone kind is introduced and analyzed.

On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations

In this note we study the convergence of monotoneP1 finite element methods on unstructuredmeshes for fully nonlinear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic diffusions. Using elliptic projection operators we treat discretisations which violate the consistency conditions of the framework by Barles and Souganidis. Weob...

L2(H1 ) finite element convergence for degenerate isotropic γ Hamilton–Jacobi–Bellman equations

Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients | SIAM Journal on Numerical Analysis | Vol. 52, No. 2 | Society for Industrial and Applied Mathematics

We propose an hp-version discontinuous Galerkin finite element method for fully nonlinear second-order elliptic Hamilton–Jacobi–Bellman equations with Cordes coefficients. The method is proved to be consistent and stable, with convergence rates that are optimal with respect to mesh size, and suboptimal in the polynomial degree by only half an order. Numerical experiments on problems with nonsmo...