Symmetric finite volume discretizations for parabolic problems.
type: Item
instance of: scholarly article
title: Symmetric finite volume discretizations for parabolic problems.
zbMATH Open document ID: 1038.65079
DOI: 10.1016/S0045-7825(03)00430-4
author: Xiuling Ma
author: Shi Shu
author: Aihui Zhou
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2004-01-23T00:00:00Z
review text: The paper deals with the following parabolic problem \[ \begin{aligned} u_t - \nabla (A \nabla u) + \alpha u = f, &\quad (x,t) \in \Omega \times (0,T],\tag{1}\\ u(x,0) = u_0(x), &\quad x \in \Omega,\tag{2}\\ u(x,t) = 0, &\quad (x,t) \in \partial \Omega \times (0,T],\tag{3} \end{aligned} \] where \(\Omega \subset R^2\) is a convex polygonal domain with boundary \(\partial \Omega\), \(u_0(x) \in L^2 (\Omega)\). The authors present and analyze one semi-discrete symmetric finite volume scheme and two full discrete symmetric finite volume schemes for (1)--(3). It is shown that these schemes preserve the symmetry of the original problem and also possess the advantages of the standard finite volume schemes. Adequate numerical examples are presented.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2031340
zbMATH Keywords: finite volume method
zbMATH Keywords: semidiscreteization
zbMATH Keywords: symmetric scheme
zbMATH Keywords: numerical examples
zbMATH Keywords: full discretization
reviewed by: Emil Minchev
MaRDI profile type: Publication
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full work available at URL: s0045-7825(03)00430-4
OpenAlex ID: W2033718206
description: scientific article; zbMATH DE number 2031340