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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations

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

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Abstract

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.