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Volume 20, Issue 5
On the Finite Volume Element Version of Ritz-Volterra Projection and Applications to Related Equations

Tie Zhang, Yan-Ping Li & Robert J. Tait

J. Comp. Math., 20 (2002), pp. 491-504.

Published online: 2002-10

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  • 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.

  • Keywords

Finite volume element, Ritz-Volterra projection, Integro-differential equations, Error analysis.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-491, author = {Zhang , TieLi , Yan-Ping and Tait , Robert J.}, title = {On the Finite Volume Element Version of Ritz-Volterra Projection and Applications to Related Equations}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8934.html} }
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.

Zhang , TieLi , Yan-Ping and Tait , Robert J.. (2002). On the Finite Volume Element Version of Ritz-Volterra Projection and Applications to Related Equations. Journal of Computational Mathematics. 20 (5). 491-504. doi:
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