TY - JOUR T1 - On the Finite Volume Element Version of Ritz-Volterra Projection and Applications to Related Equations AU - Zhang , Tie AU - Li , Yan-Ping AU - Tait , Robert J. JO - Journal of Computational Mathematics VL - 5 SP - 491 EP - 504 PY - 2002 DA - 2002/10 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8934.html KW - Finite volume element, Ritz-Volterra projection, Integro-differential equations, Error analysis. AB -

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.