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 - <p style="text-align: justify;">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.</p>