Stability and accuracy of spatial approximations for wave equation tidal models
type: Item
instance of: scholarly article
title: Stability and accuracy of spatial approximations for wave equation tidal models
zbMATH Open document ID: 0573.76020
DOI: 10.1016/0021-9991(85)90030-0
author: Ingemar P. E. Kinnmark
author: William G. Gray
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: Amplitude and phase characteristics for numerical approximations to the shallow water wave equation are obtained for linear and quadratic finite elements, for finite difference approximations, for non-constant bathemetry, and for uneven node spacing. Stability is shown to require non-zero friction as well as satisfaction of a Courant constraint. Lumping is shown to reduce the Courant constraint for stability while higher order and quadratic finite element approximations require a more restrictive constraint than their second order and linear finite element counterparts. The amplitude of the propagation factor for stable schemes and propagating waves is seen to be independent of the Courant number and type of numerical approximation. Although the higher order and quadratic schemes provide better propagation of the low and moderate frequency waves, the highest frequency waves (2\(\Delta\) x) are better propagated by low order numerical methods.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3915842
zbMATH Keywords: linear finite elements
zbMATH Keywords: stability of numerical schemes
zbMATH Keywords: Amplitude and phase characteristics
zbMATH Keywords: shallow water wave equation
zbMATH Keywords: quadratic finite elements
zbMATH Keywords: finite difference approximations
zbMATH Keywords: non-constant bathemetry
zbMATH Keywords: uneven node spacing
zbMATH Keywords: non-zero friction
zbMATH Keywords: Courant constraint
MaRDI profile type: Publication
full work available at URL: 0021-9991(85)90030-0
OpenAlex ID: W2052197741
cites work: Q3716534
cites work: A two-dimensional analysis of the wave equation model for finite element tidal computations
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description: scientific article; zbMATH DE number 3915842