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Incompressible Materials and Flow Problems

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Mixed Finite Element Methods and Applications

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 44))

Abstract

Although the approximation of incompressible flows by finite element methods has grown quite independently of the main stream of mixed and hybrid methods, it was soon recognised that a precise analysis requires the framework of mixed methods. In many cases, one may directly apply the techniques and results of Chaps. 4 and 5. In particular, the elements used are often standard elements or simple variants of standard elements. The specificity of the Stokes problem has however led to the development of special techniques; we shall present some of them that seem particularly interesting. Throughout this study, the main point will be to make a clever choice of elements leading to the satisfaction of the inf-sup condition which is here the important one as coercivity considerations are almost always straightforward.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, University of Pavia, Pavia, Italy

    Daniele Boffi

  2. IUSS (Istituto Universitario di Studi Superiori), Pavia, Italy

    Franco Brezzi

  3. Département de mathématiques et de statistique, Université Laval, Québec, Canada

    Michel Fortin

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  1. Daniele Boffi
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  2. Franco Brezzi
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  3. Michel Fortin
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Boffi, D., Brezzi, F., Fortin, M. (2013). Incompressible Materials and Flow Problems. In: Mixed Finite Element Methods and Applications. Springer Series in Computational Mathematics, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36519-5_8

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