Volume 52, Number 1, January–February 2018
|Page(s)||99 - 122|
|Published online||15 May 2018|
Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes★
Department of Mathematics and Statistics, University of Strathclyde,
26 Richmond Street,
G1 1XH, Scotland
2 Departamento Académico de Matemáticas, ITAM, Río Hondo 1, CDMX, México
Revised: 4 May 2017
Accepted: 19 June 2017
In this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order ℚ12 × ℙ0 pair, we first identify the pressure components that make this finite element pair to be non-inf-sup stable, especially with respect to the aspect ratio. We then propose a way to penalise them, both strongly, by directly removing them from the space, and weakly, by adding a stabilisation term based on jumps of the pressure across selected edges. Concerning the velocity stabilisation, we propose an enhanced grad-div term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically.
Mathematics Subject Classification: 65N30 / 65N12 / 65N50
Key words: Oseen equation / stabilised finite element method / anisotropic quadrilateral mesh
© EDP Sciences, SMAI 2018
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