The Accuracy of a Finite-Element Vertical Discretization Scheme for Primitive Equation Models: Comparison with a Finite-Difference Scheme

Michel Béland Division de Recherche en Prévision Numé, Service de l’Enviornment Atmosphérique, Dorval, Quéc, Canada H9P 1J3

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Jean Côté Division de Recherche en Prévision Numé, Service de l’Enviornment Atmosphérique, Dorval, Quéc, Canada H9P 1J3

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Andrew Staniforth Division de Recherche en Prévision Numé, Service de l’Enviornment Atmosphérique, Dorval, Quéc, Canada H9P 1J3

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Abstract

The accuracy of a slightly modified version of the finite-element vertical discretization scheme first described in Staniforth and Daley is studied with respect to a set of Rossby and gravity analytical normal modes obtained as solutions of a linearized primitive equation model. The scheme is also compared to a second-order, staggered, finite-difference vertical discretization scheme. The results of these comparisons are in favor of the finite-element method as far as accuracy is concerned. In terms of computation time, both methods are identical.

Abstract

The accuracy of a slightly modified version of the finite-element vertical discretization scheme first described in Staniforth and Daley is studied with respect to a set of Rossby and gravity analytical normal modes obtained as solutions of a linearized primitive equation model. The scheme is also compared to a second-order, staggered, finite-difference vertical discretization scheme. The results of these comparisons are in favor of the finite-element method as far as accuracy is concerned. In terms of computation time, both methods are identical.

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