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

Jensen, Max and Smears, Iain (2013) Finite element methods with artificial diffusion for Hamilton-Jacobi-Bellman equations. In: Cangiani, Andrea, Davidchack, Ruslan L, Georgoulis, Emmanuli, Gorban, Alexander N, Levesley, Jeremy and Tretyakpv, Michael V (eds.) Numerical mathematics and advanced applications 2011: proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Springer-Verlag, Berlin, pp. 267-274. ISBN 9783642331336

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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 (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.

Item Type: Book Section
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 13:20
Last Modified: 19 Jun 2013 13:20
URI: http://sro.sussex.ac.uk/id/eprint/45510

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