Superconvergence Analysis of Finite Element Method for Onlinear Klein-Gordon Equation

Abstract

The standard finite elements of degree p over the rectangular meshes are applied to a non-linear Klein-Gordon equation. By utilizing the properties of interpolation on the element, high accuracy analysis and derivative delivery techniques with respect to time t instead of the traditional Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the supercloseproperty with order is obtained. Furthermore, the superconvergence result is derived through the postprocessing approach.