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

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • M. Jensen

    (Durham University)

  • I. Smears

    (Oxford University)

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.

Suggested Citation

  • M. Jensen & I. Smears, 2013. "Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 267-274, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_29
    DOI: 10.1007/978-3-642-33134-3_29
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