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Abstract : We propose a new discontinuous Galerkin (DG) method based on Cheng and Shu (J. Comput. Phys. Vol 223, pp. 398--415, 2007) to solve a class of Hamilton-Jacobi equations that arises from optimal control problems. These equations are connected to front propagation problems or minimal time problems with non isotropic dynamics. Several numerical experiments show the relevance of our method, in particular for front propagation.
Keywords: Hamilton-Jacobi-Bellman equations; Discontinuous Galerkin methods; Level sets;front propagation