TY - JOUR T1 - Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations AU - Zhang , Shu-Hua AU - Lin , Tao AU - Lin , Yan-Ping AU - Rao , Ming JO - Journal of Computational Mathematics VL - 4 SP - 407 EP - 422 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8993.html KW - Volterra integro-differential equations, Petrov-Galerkin finite element methods, Asymptotic expansions, Interpolation post-processing, A-posteriori error estimators. AB -

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.