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-infinity(L-2)-norm in the case of the space semidiscretization method of lines and in the case of the space time discontinuous Galerkin method in the L-2(L-2)-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. (C) 2016 Elsevier Ltd. All rights reserved.