On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations
Numerical Analysis
2013-02-25 v1 Optimization and Control
Abstract
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear 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. We obtain strong uniform convergence of the numerical solutions and, under non-degeneracy assumptions, strong L2 convergence of the gradients.
Keywords
Cite
@article{arxiv.1111.5423,
title = {On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations},
author = {Max Jensen and Iain Smears},
journal= {arXiv preprint arXiv:1111.5423},
year = {2013}
}
Comments
Keywords: Bellman equations, finite element methods, viscosity solutions, fully nonlinear operators; 18 pages, 1 figure