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Abstract
In this work we present and analyse new infsup 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 QIn this work we present and analyse new infsup 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 Q2 1 × P0 pair, we first identify the pressure components that make this finite element pair to be noninfsup 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 graddiv term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically. Q21 × P0 pair, we first identify the pressure components that make this finite element pair to be noninfsup 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 graddiv term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically.
Original language  English 

Number of pages  29 
Journal  ESAIM: Mathematical Modelling and Numerical Analysis 
DOIs  
Publication status  Accepted/In press  19 Jun 2017 
Keywords
 Oseen equation
 stabilised finite element method
 anisotropic quadrilateral mesh
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Projects
 1 Finished

Minimal stabilization procedures on anisotropic meshes and nonlinear schemes
15/09/12 → 14/09/15
Project: Research