Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations
Year: 2001
Author: Shu-Hua Zhang, Tao Lin, Yan-Ping Lin, Ming Rao
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 4 : pp. 407–422
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-8993
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 4 : pp. 407–422
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Volterra integro-differential equations Petrov-Galerkin finite element methods Asymptotic expansions Interpolation post-processing A-posteriori error estimators.