A note on the stabilised Q1-P0 method on quadrilaterals with high aspect ratios

Barrenechea, Gabriel R. and Wachtel, Andreas; Knobloch, Petr, ed. (2016) A note on the stabilised Q1-P0 method on quadrilaterals with high aspect ratios. In: Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, 108 . Springer-Verlag, CZE, pp. 1-11. ISBN 9783319257259

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    Abstract

    This work deals with the stabilisation of mixed methods for the Stokes problem on anisotropic meshes. For this, we extend a method proposed previously in Liao and Silvester (IMA J Numer Anal 33(2):413-431, 2013), to cover the case in which the mesh contains anisotropically refined corners. This modification consists of adding extra jump terms in selected edges connecting small shape regular with large anisotropic elements. We prove stability and convergence of the proposed method, and provide numerical evidence for the fact that our approach successfully removes the dependence on the anisotropy.