Convergence of discontinuous Galerkin schemes for front propagation with obstacles | Zendy

Olivier Bokanowski | Zendy; Yingda Cheng | Zendy; ChiWang Shu | Zendy

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Convergence of discontinuous Galerkin schemes for front propagation with obstacles

Author(s) -

Olivier Bokanowski,

Yingda Cheng,

ChiWang Shu

Publication year - 2015

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3072

Subject(s) - mathematics , discontinuous galerkin method , lipschitz continuity , convergence (economics) , galerkin method , mathematical analysis , nonlinear system , space (punctuation) , dimension (graph theory) , pure mathematics , finite element method , physics , quantum mechanics , economics , thermodynamics , economic growth , linguistics , philosophy

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.

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