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COMPARISON OF H AND P FINITE ELEMENT APPROXIMATIONS OF THE SHALLOW WATER EQUATIONS
Author(s) -
Walters R. A.,
Barragy E. J.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970115)24:1<61::aid-fld479>3.0.co;2-y
Subject(s) - shallow water equations , convergence (economics) , helmholtz equation , mathematics , finite element method , momentum (technical analysis) , test case , waves and shallow water , rate of convergence , mathematical analysis , helmholtz free energy , geometry , boundary value problem , geology , channel (broadcasting) , computer science , engineering , physics , computer network , statistics , oceanography , regression analysis , finance , economics , economic growth , structural engineering , quantum mechanics
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. © 1997 John Wiley & Sons, Ltd.