Iterative methods for the Poisson equation in L-shape domain based on domain decomposition method

In this paper we propose the finite difference method for the second-order elliptic equation in the L-shape domain. The scheme is based on the non-overlap domain decomposition method. We use the coarse mesh difference scheme at the interface grids and fine mesh difference scheme at the interior mesh points. We derive the error estimate O(h2 + H3) with mesh size h and coarse mesh size H. Then we discuss some iterative methods for our scheme and derive the upper bound of the convergent rate 1 − H. Finally we present some numerical experiments.