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 ∞ ( 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.

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