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Library of Congress Cataloging in PublicationData Thomasset, Frani,(ois. Implementation of finite element for Navier-Stokes equations. (Springer series in computational physics) I. Fluid dynamics. 2. Navier-Stokes equations-Numerical solutions. 3. Finite element method. I. Title. II. Series. QA911.T46 515.3'53 81-9169 AACR2

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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)

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