Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Bokanowski, Olivier; Cheng, Yingda; Shu, Chi-Wang

doi:10.1090/mcom/3072

Convergence of discontinuous Galerkin schemes for front propagation with obstacles
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by Olivier Bokanowski, Yingda Cheng and Chi-Wang Shu;

Math. Comp. 85 (2016), 2131-2159

DOI: https://doi.org/10.1090/mcom/3072

Published electronically: December 29, 2015

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Abstract:

We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge-Kutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form $\min (u_t + c u_x, u - g(x))=0$, in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These “low regularity” assumptions are the natural ones for the solutions of the studied equations. Numerical tests are given to illustrate the behavior of our schemes.

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