Discontinuous Galerkin method for the solution of a transport level-set problem

The subject of the paper is the numerical analysis of the transport level-set problem discretized by the discontinuous Galerkin method. Without the assumption that the first order nonstationary transport equation contains a reaction term, which is used in a standard literature, we prove error estimates in the L∞(L2)L∞(L2)-norm in the case of the space semidiscretization method of lines and in the case of the space–time discontinuous Galerkin method in the L2(L2)L2(L2)-norm. Numerical experiments support the derived error estimates and show that they are not sharp in the case of the space–time discontinuous Galerkin method.