A generalized (meshfree) finite difference discretization for elliptic interface problems

The aim of this paper is twofold. First, two generalized (meshfree) finite difference methods (GFDM) for the Poisson equation are discussed. These are methods due to Liszka and Orkisz (1980) [10] and to Tiwaxi (2001) [7]. Both methods are based on using moving least squares (MLS) approach for deriving the discretization. The relative comparison shows, that the second method is preferable because it is less sensitive to the topological restrictions on the nodes distribution. Next, an extension of the second method is presented, which allows for accounting for internal interfaces, associated with discontinuous coefficients. Results from numerical experiments illustrate the second order convergence of the proposed GFDM for interface problems.