MacKenzie, John and Nicola, Aurelian (2007) A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations. SIAM Journal on Scientific Computing, 29 (6). pp. 2258-2282. ISSN 1064-8275
In this paper we consider the numerical solution of first-order Hamilton-Jacobi equations using the combination of a discontinuous Galerkin finite element method and an adaptive $r$-refinement (mesh movement) strategy. Particular attention is given to the choice of an appropriate adaptivity criterion when the solution becomes discontinuous. Numerical examples in one and two dimensions are presented to demonstrate the effectiveness of the adaptive procedure.
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