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Improved finite element forms for the shallow‐water wave equations
Author(s) -
Williams R. T.,
Zienkiewicz O. C.
Publication year - 1981
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/fld.1650010107
Subject(s) - finite element method , fourier transform , mathematics , waves and shallow water , shallow water equations , mathematical analysis , mixed finite element method , extended finite element method , basis (linear algebra) , smoothed finite element method , finite difference , basis function , fourier transform on finite groups , geometry , fourier analysis , physics , engineering , boundary knot method , structural engineering , fractional fourier transform , boundary element method , thermodynamics
This paper presents new finite element formulations of the shallow‐water wave equations which use different basis functions for the velocity and height fields. These arrangements are analysed with the Fourier transform technique which was developed by Schoenstadt, 1 and they are also compared with other finite difference and finite element schemes. The new schemes are integrated in time for two initial states and compared with analytic solutions and numerical solutions from other schemes. The behaviour of the new forms is excellent and they are also convenient to apply in two dimensions with triangular elements.