Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Olivier Bokanowski; Yingda Cheng; Chi-Wang Shu

Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Numerical Analysis 2015-03-02 v2

Authors: Olivier Bokanowski , Yingda Cheng , Chi-Wang Shu

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.

Keywords

discontinuous Galerkin schemes front propagation obstacle problems Hamilton-Jacobi equations semi-Lagrangian methods Runge-Kutta methods convergence analysis error bounds

Cite

@article{arxiv.1409.6692,
  title  = {Convergence of discontinuous Galerkin schemes for front propagation with obstacles},
  author = {Olivier Bokanowski and Yingda Cheng and Chi-Wang Shu},
  journal= {arXiv preprint arXiv:1409.6692},
  year   = {2015}
}

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28 pages

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