How to save a bad element with weak boundary conditionsHanert, E. and Legat, V. (2006) How to save a bad element with weak boundary conditions. Computers & Fluids, 35 (5). pp. 477-484. Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. Abstract/SummaryThe P-1-P-1 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 P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.
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