Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.
type: Item
instance of: scholarly article
title: Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.
zbMATH Open document ID: 1274.65251
author: Abdallah Bradji
author: Jürgen Fuhrmann
published in: Applications of Mathematics
publication date: 2013-05-13T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143131
review text: The article is concerned with the derivation of error estimates for a finite volume scheme applied to the nonstationary heat equation with homogeneous boundary conditions. The space-time discretization employs the discrete gradient construction from the so-called SUSHI scheme of \textit{R. Eymard} et al. [IMA J. Numer. Anal. 30, 1009--1043 (2010; Zbl 1202.65144)], originally applied to stationary elliptic problems. Such a scheme can be applied and analyzed on very general nonconforming meshes with star-shaped polyhedral elements. Error estimates in the \(L^{\infty }(H^1_0)\) and \(W^{1,\infty }(L^2)\) norms are derived. The proof uses estimates of the discrete gradient and properties of the involved discrete spaces from [loc. cit.]. Moreover, a suitable auxiliary problem is introduced, for which error estimates are known, and the final results of the paper are derived by comparison of the auxiliary problem and the considered finite volume scheme. The error estimates are derived under rather strong regularity assumptions on the exact solution.
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 6162811
zbMATH Keywords: finite volume method
zbMATH Keywords: heat equation
zbMATH Keywords: error estimate
zbMATH Keywords: discrete gradient
zbMATH Keywords: nonconforming grids
zbMATH Keywords: star-shaped elements
zbMATH Keywords: SUSHI scheme
MaRDI profile type: Publication
OpenAlex ID: W2039783631
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DOI: 10.1007/S10492-013-0001-Y
description: scientific article; zbMATH DE number 6162811