Volume 23, Issue 2
Finite Volume Numerical Analysis for Parabolic Equation with Robin Boundary Condition

J. Comp. Math., 23 (2005), pp. 165-176.

Published online: 2005-04

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• Abstract

In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of $R^d$ ($d = 2$ or $3$) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and $L^2$ and $H^1$ spacial norm convergence properties are obtained.

• Keywords

Finite volume, Parabolic convection diffusion equations, Numerical analysis.

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@Article{JCM-23-165, author = {}, title = {Finite Volume Numerical Analysis for Parabolic Equation with Robin Boundary Condition}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {2}, pages = {165--176}, abstract = {

In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of $R^d$ ($d = 2$ or $3$) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and $L^2$ and $H^1$ spacial norm convergence properties are obtained.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8804.html} }
TY - JOUR T1 - Finite Volume Numerical Analysis for Parabolic Equation with Robin Boundary Condition JO - Journal of Computational Mathematics VL - 2 SP - 165 EP - 176 PY - 2005 DA - 2005/04 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8804.html KW - Finite volume, Parabolic convection diffusion equations, Numerical analysis. AB -

In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of $R^d$ ($d = 2$ or $3$) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and $L^2$ and $H^1$ spacial norm convergence properties are obtained.

Xia Cui. (1970). Finite Volume Numerical Analysis for Parabolic Equation with Robin Boundary Condition. Journal of Computational Mathematics. 23 (2). 165-176. doi:
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