On the Finite Volume Element Version of Ritz-Volterra Projection and Applications to Related Equations
Year: 2002
Author: Tie Zhang, Yan-Ping Li, Robert J. Tait
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 5 : pp. 491–504
Abstract
In this paper, we present a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal $L_2$ and $H^1$ norm error estimates, and the $L_\infty$ and $W^1_\infty$ norm error estimates by means of the time dependent Green functions. Our discussions also include elliptic and parabolic problems as the special cases.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JCM-8934
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 5 : pp. 491–504
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Finite volume element Ritz-Volterra projection Integro-differential equations Error analysis.