Superconvergence analysis of anisotropic linear triangular finite element for nonlinear Schrödinger equation

The main aim of this paper is to apply the simplest anisotropic linear triangular finite element to solve the nonlinear Schrödinger equation (NLS). Firstly, the error estimate and superclose property with order O(h2)O(h2) about the Ritz projection are given based on an anisotropic interpolation property and high accuracy analysis of this element. Secondly, through establishing the relationship between the Ritz projection and interpolation, the superclose property of the interpolation is received. Thirdly, the global superconvergence with order O(h2)O(h2) is derived by use of the interpolation post-processing technique. Finally, a numerical example is provided to verify the theoretical results. It is noteworthy that the main results obtained for anisotropic meshes herein cannot be deduced by only employing the interpolation or Ritz projection.