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Preprint-No.: <   354   >   Published in: December 2012   PDF-File: IGPM354_k.pdf
Title:Analysis of a Discontinuous Galerkin Method Applied to the Level Set Equation
Authors:Eva Loch
Abstract. In this paper we investigate an error analysis of the DG method in space and the Crank-Nicolson scheme in time applied to the level set equation.The exact solution is assumed to be sufficiently smooth. Under certain assumption on the underlying velocity field we proof an error bound of order hk+1/2 + ∆t2 for the error between the exact solution and the fully discrete solution in the L2-norm , where h is the spatial gird size, ∆t the time step size and k the polynomial degree.
Keywords:finite element, Discontinuous Galerkin, upwind flux, level set method