  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.
