How to save a bad element with weak boundary conditions

Hanert, E.; Legat, V.

doi:10.1016/j.compfluid.2005.02.005

How to save a bad element with weak boundary conditions

Hanert, E.; Legat, V. (2006). How to save a bad element with weak boundary conditions. Comput. fluids 35(5): 477-484. http://dx.doi.org/10.1016/j.compfluid.2005.02.005

In: Computers & Fluids. Elsevier: New York. ISSN 0045-7930; e-ISSN 1879-0747, meer

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VLIZ: Open Marine Archive 280320 [ download pdf ]

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Second-generation Louvain-la-Neuve Ice-ocean Model, meer

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Hanert, E., meer Legat, V., meer

Abstract

The P₁–P₁ finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P₁–P₁ and

–P₁ mixed formulations. Steady and transient test cases are considered. We observe that the P₁–P₁ element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes.

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