Abstract
In this work, we present some numerical approximations for a shallow water problem with a depth-mean velocity formulation and we give, where possible, an error bound. To prove the existence of solutions, we build a sequence of approximated solutions with the Galerkin method for the momentum equation and solve the continuity equation with the method of the characteristics. This leads to an expensive natural numerical scheme. Then, in order to reduce the CPU time, we present other numerical approximations based on the linear or nonlinear Galerkin method.
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