Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations

Abstract

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.