Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations

In this note, we reinterpret a discontinuous Galerkin method originally developed by Huand Shu [1] (see also [2]) for solving Hamilton-Jacobi equations. By this reinterpretation,numerical solutions will automatically satisfy the curl-free property of the exact solutionsinside each element. This new reinterpretation allows a method of lines formulation, whichrenders a more natural framework for stability analysis. Moreover, this reinterpretation ren-ders a significantly simplified implementation with reduced cost, as only a smaller subspaceof the original solution space in [1, 2] is used and the least square procedure used in [1, 2] iscompletely avoided.References[1] C. Hu and C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton-Jacobi equations, SIAM Journal on Scientific Computing, v21 (1999), pp.666-690.[2] O. Lepsky, C. Hu and C.-W. Shu, Analysis of the discontinuous Galerkin method forHamilton-Jacobi equations, Applied Numerical Mathematics, v33 (2000), pp.423-434.