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

Gabriel R. Barrenechea; Andreas Wachtel

doi:10.1007/978-3-319-25727-3_1

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

Gabriel R. Barrenechea^*, Andreas Wachtel

^*Corresponding author for this work

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

1 Citation (Scopus)

28 Downloads (Pure)

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 language	English
Title of host publication	Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014
Editors	Petr Knobloch
Place of Publication	Cham
Publisher	Springer-Verlag
Pages	1-11
Number of pages	11
Volume	108
ISBN (Print)	9783319257259
DOIs	https://doi.org/10.1007/978-3-319-25727-3_1
Publication status	Published - 20 Apr 2016
Event	Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014 - Prague, Czech Republic Duration: 15 Sept 2014 → 19 Sept 2014

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	108
ISSN (Print)	1439-7358

Conference

Conference	Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014
Country/Territory	Czech Republic
City	Prague
Period	15/09/14 → 19/09/14

Keywords

high aspect ratios
anisotropic meshes
anisotropy

Access to Document

10.1007/978-3-319-25727-3_1

Barrenechea-Wachtel-LNCS-2016-method-on-quadrilaterals-with-high-aspect-ratiosAccepted author manuscript, 185 KB

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). Springer-Verlag. https://doi.org/10.1007/978-3-319-25727-3_1

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Barrenechea, GR & 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, Lecture Notes in Computational Science and Engineering, vol. 108, Springer-Verlag, Cham, pp. 1-11, Internatinal Conference on Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2014, Prague, Czech Republic, 15/09/14. https://doi.org/10.1007/978-3-319-25727-3_1

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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