Wave propagation in quadratic-finite-element approximations to hyperbolic equations
type: Item
instance of: scholarly article
title: Wave propagation in quadratic-finite-element approximations to hyperbolic equations
zbMATH Open document ID: 0958.65097
author: Dale R. Durran
published in: Journal of Computational Physics
publication date: 2000-11-23T00:00:00Z
review text: The author discusses the dispersion relation for discretization of the wave equation \(u_t + c u_x = 0\) by the method of lines derived from application of the finite-element method with quadratic basis functions. For many discretizations of this wave equation the dispersion function is periodic with period \(2 \pi\), but in this case the period is \(4 \pi\). On an interval of length \(2 \pi\) one obtains what appear to be two dispersion relations, but they map into each other under a translation by~\(2 \pi\).
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 1443380
zbMATH Keywords: quadratic finite elements
zbMATH Keywords: linear wave equation
zbMATH Keywords: method of lines
zbMATH Keywords: dispersion function
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
full work available at URL: jcph.2000.6453
OpenAlex ID: W2071468043
cites work: The use of quadratic finite element methods and irregular grids in the solution of hyperbolic problems
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cites work: Q4255433
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cites work: The group velocity of some numerical schemes
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DOI: 10.1006/JCPH.2000.6453
description: scientific article; zbMATH DE number 1443380