Extrapolation of the Finite Element Method on General Meshes

Abstract

In this paper, we consider the extrapolation method for second order elliptic problems on general meshes and derive a type of finite element expansion which is dependent of the triangulation. It allows to prove the effectiveness of the extrapolation on general meshes and also validates the extrapolation method can be applied on the automatically produced meshes of the general computing domains. Some numerical examples are given to illustrate the theoretical analysis.