Local discontinuous Galerkin method for elliptic interface problems

In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains. The interface may be arbitrary smooth curves. It is shown that the error estimates in L2-norm for the solution and the flux are O(h2|logh|) and O(h|logh1/2), respectively. In numerical experiments, the successive substitution iterative methods are used to solve the LDG schemes. Numerical results verify the efficiency and accuracy of the method.