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

journal contribution
posted on 2023-06-08, 15:16 authored by Max Jensen, Iain Smears
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.

History

Publication status

  • Published

Journal

SIAM Journal on Numerical Analysis (SINUM)

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

1

Volume

51

Page range

137-162

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-06-19

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