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Numerical Algorithms

, Volume 61, Issue 3, pp 465–478 | Cite as

A two-level local projection stabilisation on uniformly refined triangular meshes

  • Gunar Matthies
  • Lutz Tobiska
Original Paper

Abstract

The two-level local projection stabilisation on triangular meshes is based on the refinement of a macro cell into three child cells by connecting the barycentre with the vertices of the macro cell. This refinement technique leads to non-nested meshes with large inner angles and to non-nested finite element spaces. We show that also the red refinement where a triangle is divided into four child cells by connecting the midpoints of the edges can be used. This avoids the above mentioned disadvantages. For the red refinement a local inf-sup condition for the continuous, piecewise polynomial approximation spaces of order less than or equal to r ≥ 2 living on the refined mesh and discontinuous, piecewise polynomial projection spaces of order less than or equal to r − 1 living on the coarser mesh is established. Numerical tests compare the local projection stabilisation resulting from both refinement rules in case of convection-diffusion problems.

Keywords

Stabilised finite elements Local projection stabilisation 

Mathematics Subject Classifications (2010)

65N12 65N30 65N15 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Fachbereich 10 Mathematik und Naturwissenschaften, Institut für MathematikUniversität KasselKasselGermany
  2. 2.Institut für Analysis und NumerikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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