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Finite element solution for the transcritical shallow‐water equations
Author(s) -
Goutal Nicole,
Nedelec J. C.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110407
Subject(s) - mathematics , convergence (economics) , finite element method , operator (biology) , mathematical analysis , acceleration , classical mechanics , biochemistry , chemistry , physics , repressor , gene , transcription factor , economics , thermodynamics , economic growth
Abstract A new solution of the two‐dimensional shallow‐water equations, using a finite element method is described. The formulation is based on the velocity and height variables and follows two steps. In the first step, the convective terms are solved by a characteristic method and in the second step the propagative and diffusion terms are taken into account. The close relation between the latter operator and a Stokes penalized problem is shown; an algorithm of Uzawa type is then used for its solution. Acceleration convergence is obtained by preconditioning, and new methods are presented, the quality of the convergence being shown on application to some sample tests. The overall method has revealed quite efficient and application to industrial cases is already planned.