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Solving shallow water equations by a mixed implicit finite element method. (English) Zbl 0713.76069
Summary: The shallow water equations are solved by using a numerical scheme implicit in time, and finite elements of P. A. Raviart and J. M. Thomas [Math. Aspects Finite Elem. Meth., Proc. Conf. Rome 1975, Lect. Notes Math. 606, 292-315 (1977; Zbl 0362.65089)] for the space discretization. The nonlinear discretized problem is solved by a duality iterative algorithm. Numerical results for the dam break test problem and for simulation of real tidal currents are given.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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