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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.

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