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Finite element methods with artificial diffusion for Hamilton-Jacobi-Bellman equations

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posted on 2023-06-08, 15:16 authored by Max Jensen, Iain Smears
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 (Jensen and Smears, On the convergence of finite element methods for Hamilton-Jacobi-Bellman equations, arxiv:1111.5423, 2011); 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.

History

Publication status

  • Published

File Version

  • Submitted version

Publisher

Springer-Verlag

Page range

267-274

Pages

859.0

Book title

Numerical mathematics and advanced applications 2011: proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011

Place of publication

Berlin

ISBN

9783642331336

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Editors

Ruslan L Davidchack, Jeremy Levesley, Emmanuli Georgoulis, Michael V Tretyakpv, Andrea Cangiani, Alexander N Gorban

Legacy Posted Date

2013-06-19

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