On the convergence of finite element methods for Hamilton-Jacobi-Bellman equations

Jensen, Max and Smears, Iain (2013) On the convergence of finite element methods for Hamilton-Jacobi-Bellman equations. SIAM Journal on Numerical Analysis (SINUM), 51 (1). pp. 137-162. ISSN 0036-1429

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 19 Jun 2013 11:30
Last Modified: 28 Mar 2017 05:22
URI: http://sro.sussex.ac.uk/id/eprint/45507

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