Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations
Numerical Analysis
2013-02-25 v2 Optimization and Control
Abstract
In this short note we investigate the numerical performance of the method of artificial diffusion for second-order fully nonlinear Hamilton-Jacobi-Bellman equations. The method was proposed in (M. Jensen and I. Smears, arxiv:1111.5423); where a framework of finite element methods for Hamilton-Jacobi-Bellman equations was studied theoretically. The numerical examples in this note study how the artificial diffusion is activated in regions of degeneracy, the effect of a locally selected diffusion parameter on the observed numerical dissipation and the solution of second-order fully nonlinear equations on irregular geometries.
Cite
@article{arxiv.1201.3581,
title = {Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations},
author = {Max Jensen and Iain Smears},
journal= {arXiv preprint arXiv:1201.3581},
year = {2013}
}
Comments
Enumath 2011, version 2 contains in addition convergence rates