Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations

M. Jensen () and I. Smears ()
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M. Jensen: Durham University
I. Smears: Oxford University

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 267-274 from Springer

Abstract: 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.

Keywords: Eikonal Equation; Numerical Dissipation; Bound Lipschitz Domain; Dynamic Programming Principle; Artificial Diffusion (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_29

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DOI: 10.1007/978-3-642-33134-3_29

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