Unified construction and \(L^2\) analysis for the finite volume element method over tensorial meshes
type: Item
instance of: scholarly article
title: Unified construction and \(L^2\) analysis for the finite volume element method over tensorial meshes
zbMATH Open document ID: 1506.65190
author: Xiang Wang
author: Yuqing Zhang
published in: Advances in Computational Mathematics
publication date: 2023-01-17T00:00:00Z
review text: The authors provide the construction and analysis for a family of high order FVE (Finite Volume Element) schemes with the optimal \(L^2\) convergence rate over tensorial meshes in any \(d\)-dimension with \(d\geq 2\). This family includes for instance the existing Gaussian point-based schemes. At the same time, different dual strategies could be allowed in different directions, and the dual strategies could also be asymmetric within each primary tensorial element. This makes it possible to apply FVE scheme to some complex problems. The definition of the tensorial orthogonal condition (TOC) over tensorial meshes in \(d\)-dimension is proposed and analyzed. It is proved that that all the FVE schemes derived from the TOC hold the optimal \(L^2\) convergence rate. Some numerical tests are presented to support the theoretical results.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N08
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 7643020
zbMATH Keywords: finite volume
zbMATH Keywords: tensorial mesh
zbMATH Keywords: \(L^2\) estimate
zbMATH Keywords: orthogonal condition
MaRDI profile type: Publication
full work available at URL: s10444-022-10004-0
OpenAlex ID: W4313408978
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DOI: 10.1007/S10444-022-10004-0
description: scientific article; zbMATH DE number 7643020