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Erschienen in:
2021 | OriginalPaper | Buchkapitel
30. Stokes equations: Basic ideas
verfasst von : Alexandre Ern, Jean-Luc Guermond
Erschienen in: Finite Elements II
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Abstract
The Stokes equations constitute the basic linear model for incompressible fluid mechanics. We first derive a weak formulation of the Stokes equations and establish its well-posedness. The approximation is then realized by means of mixed finite elements, that is, we consider a pair of finite elements, where the first component of the pair is used to approximate the velocity and the second component is used to approximated the pressure. In this chapter, we list some classical unstable pairs. Examples of stable pairs are reviewed in the next two chapters.