Stability and phase speed for various finite element formulations of the advection equation
type: Item
instance of: scholarly article
title: Stability and phase speed for various finite element formulations of the advection equation
zbMATH Open document ID: 0613.76099
DOI: 10.1016/0045-7930(86)90014-9
author: Beny Neta
author: R. T. Williams
published in: Computers and Fluids
publication date: 1986-01-01T00:00:00Z
review text: This paper analyzes the stability and accuracy of various finite element approximations to the linearized two-dimensional advection equation. Four triangular elements with linear basis functions are included along with a rectangular element with bilinear basis functions. In addition, second- and fourth-order finite difference schemes are examined for comparison. Time is discretized with the leapfrog method. The criss-cross triangle formulation is found to be unstable. The best schemes are the isosceles triangles with linear basis functions and the rectangles with bilinear basis functions.
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3993198
zbMATH Keywords: stability
zbMATH Keywords: accuracy
zbMATH Keywords: finite element approximations
zbMATH Keywords: linearized two- dimensional advection equation
zbMATH Keywords: triangular elements
zbMATH Keywords: fourth-order finite difference schemes
zbMATH Keywords: leapfrog method
zbMATH Keywords: criss-cross triangle formulation
MaRDI profile type: Publication
full work available at URL: 0045-7930(86)90014-9
OpenAlex ID: W1997459334
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description: scientific article; zbMATH DE number 3993198