Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Olivier Bokanowski Universite Denis-Diderot Paris 7 Yingda Cheng Michigan State University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25020

Mathematics of Computation, 85, 2131-2159, 2016
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.
Hamilton-Jacobi-Bellman equations; discontinuous Galerkin methods; level sets; front propagation; obstacle problems; dynamic programming principle; convergence
[ Download ] [ 2016-10-11 11:16:17 uploaded by chiwangshu ] [ 765 downloads ] [ 0 comments ] [ Cited by 3 ]
@inproceedings{olivier2016convergence,
  title={Convergence of discontinuous Galerkin schemes for front propagation with obstacles},
  author={Olivier Bokanowski, Yingda Cheng, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011111617389765134},
  booktitle={Mathematics of Computation},
  volume={85},
  pages={2131-2159},
  year={2016},
}
Olivier Bokanowski, Yingda Cheng, and Chi-Wang Shu. Convergence of discontinuous Galerkin schemes for front propagation with obstacles. 2016. Vol. 85. In Mathematics of Computation. pp.2131-2159. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011111617389765134.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved