Jensen, M;
Smears, I;
Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations.
In: Cangiani, Andrea and Davidchack, Ruslan L. and Georgoulis, Emmanuil and Gorban, Alexander N. and Levesley, Jeremy and Tretyakov, Michael V., (eds.)
Proceedings of Numerical Mathematics and Advanced Applications 2011.
(pp. pp. 267-274).
Springer: Berlin, Heidelberg.
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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.
| Type: | Proceedings paper |
|---|---|
| Title: | Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations |
| Event: | Numerical Mathematics and Advanced Applications 2011. |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-642-33134-3_29 |
| Publisher version: | http://dx.doi.org/10.1007/978-3-642-33134-3_29 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Eikonal Equation, Numerical Dissipation, Bound Lipschitz Domain, Dynamic Programming Principle, Artificial Diffusion |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1572498 |
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