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Convergence of discontinuous Galerkin schemes for front propagation with obstacles

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.

preprint2015arXivOpen access
Olivier BokanowskiYingda ChengChi-Wang Shu
math.NA
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Olivier BokanowskiYingda ChengChi-Wang Shu

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