A noise-free finite element scheme for the two-layer shallow water equations

Abstract

A semi-implicit time marching scheme is combined with triangular finite elements in space for the discretization of the two-layer shallow water equations. Velocity variables are approximated by so-called non-conforming linear elements, which have their nodes at mid-sides of the triangles. Height variables are approximated by linear conforming elements. The resulting discrete scheme is easily inverted and is free of two-grid oscillation problems. It is identical for a particular lattice to a finite difference scheme derived by Mesinger (1973)