Convergence of discontinuous Galerkin schemes for front propagation with obstacles

28 pagesWe study semi-Lagrangian discontinuous Galerkin (SLDG) andRunge-Kutta discontinuous Galerkin (RKDG) schemes for somefront propagation problems in the presence of an obstacle term, modeled by a nonlinearHamilton-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