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.
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References
G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, J. Asymptotic Analysis, 4:271–283, 1991.
X. Feng and R. Glowinsky and M. Neilan, Recent developments in numerical methods for fully nonlinear second order partial differential equations, submitted to SIAM Review.
X. Feng and M. Neilan, The vanishing moment method for fully nonlinear second order partial differential equations: formulation, theory, and numerical analysis, arXiv:1109.1183, 2011.
M. Jensen and I. Smears, On the convergence of finite element methods for Hamilton-Jacobi-Bellman equations, arXiv:1111.5423, 2011.
H.J. Kushner and P. Dupuis, Numerical methods for stochastic control problems in continuous time, Applications of Mathematics 24, Springer-Verlag, 2001.
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Jensen, M., Smears, I. (2013). Finite Element Methods with Artificial Diffusion for Hamilton-Jacobi-Bellman Equations. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_29
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DOI: https://doi.org/10.1007/978-3-642-33134-3_29
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