|| IGPM354.pdf December 2012 |
|| Analysis of a Discontinuous Galerkin Method Applied to the Level Set Equation |
||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.
|| finite element, Discontinuous Galerkin, upwind flux, level set method |