Abstract:We propose a high‐order curvilinear Lagrangian finite element method for shallow water hydrodynamics. This method falls into the high‐order Lagrangian framework using curvilinear finite elements. We discretize the position and velocity in continuous finite element spaces. The high‐order finite element basis functions are defined on curvilinear meshes and can be obtained through a high‐order parametric mapping from a reference element. Considering the variational formulation of momentum conservation, the global… Show more
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