Pré-Publication, Document De Travail Année : 2014

Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Résumé

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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Dates et versions

hal-00834342 , version 1 (14-06-2013)
hal-00834342 , version 2 (23-09-2014)
hal-00834342 , version 3 (25-02-2015)

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Olivier Bokanowski, Yingda Cheng, Chi-Wang Shu. Convergence of discontinuous Galerkin schemes for front propagation with obstacles. 2014. ⟨hal-00834342v3⟩
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