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COMPARISON OF H AND P FINITE ELEMENT APPROXIMATIONS OF THE SHALLOW WATER EQUATIONS

โœ Scribed by R. A. Walters; E. J. Barragy

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
498 KB
Volume
24
Category
Article
ISSN
0271-2091

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โœฆ Synopsis

A p-type finite element scheme is introduced for the three-dimensional shallow water equations with a harmonic expansion in time. The wave continuity equation formulation is used which decouples the problem into a Helmholtz equation for surface elevation and a momentum equation for horizontal velocity. An exploration of the applicability of p methods to this form of the shallow water problem is presented, with a consideration of the problem of continuity errors. The convergence rates and relative computational efficiency between h-and p-type methods are compared with the use of three test cases representing various degrees of difficulty. A channel test case establishes convergence rates, a continental shelf test case examines a problem with accuracy difficulties at the shelf break, and a field-scale test case examines problems with highly irregular grids. For the irregular grids, adaptive h combined with uniform p refinement was necessary to retain high convergence rates.

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