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

Gabriel R. Barrenechea, Andreas Wachtel

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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.

Original languageEnglish
Title of host publicationBoundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014
EditorsPetr Knobloch
Place of PublicationCham
PublisherSpringer-Verlag
Pages1-11
Number of pages11
Volume108
ISBN (Print)9783319257259
DOIs
Publication statusPublished - 20 Apr 2016
EventInternatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014 - Prague, Czech Republic
Duration: 15 Sep 201419 Sep 2014

Publication series

NameLecture Notes in Computational Science and Engineering
Volume108
ISSN (Print)1439-7358

Conference

ConferenceInternatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
CountryCzech Republic
CityPrague
Period15/09/1419/09/14

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Keywords

  • high aspect ratios
  • anisotropic meshes
  • anisotropy

Cite this

Barrenechea, G. R., & Wachtel, A. (2016). A note on the stabilised Q1-P0 method on quadrilaterals with high aspect ratios. In P. Knobloch (Ed.), Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014 (Vol. 108, pp. 1-11). (Lecture Notes in Computational Science and Engineering; Vol. 108). Cham: Springer-Verlag. https://doi.org/10.1007/978-3-319-25727-3_1