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A nonlinear Galerkin method for the shallow-water equations on periodic domains. (English) Zbl 1002.76087
Summary: A nonlinear Galerkin method for the shallow-water equations is developed based on spectral transforms. The scheme is compared to a pseudo-spectral Galerkin method. Numerical results indicate that the nonlinear scheme has the potential advantage of providing similar accuracy at a lower cost than Galerkin method. The nonlinear method has also less restrictive stability conditions.

MSC:
76M22 Spectral methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
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