Superconvergence of Finite Element Methods for Linear Quasi-hyperbolic Integro-differential Equations

Abstract

We consider finite element methods applied to a class of quasi-hyperbolic integro-differential equations. Global strong super convergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. We employ a special method for initial value selection to study super convergence of the error. Two order super convergence results are demonstrated.