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Convergence of discontinuous Galerkin schemes for front propagation with obstacles

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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https://hal.inria.fr/hal-00834342
Contributor : Olivier Bokanowski <>
Submitted on : Wednesday, February 25, 2015 - 8:02:42 PM
Last modification on : Thursday, December 10, 2020 - 10:59:26 AM
Long-term archiving on: : Tuesday, May 26, 2015 - 1:41:04 PM

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  • HAL Id : hal-00834342, version 3
  • ARXIV : 1409.6692

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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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