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

Authors:
Gunar Matthies;Lutz Tobiska
Affiliations:
Fachbereich 10 Mathematik und Naturwissenschaften, Institut für Mathematik, Universität Kassel, Kassel, Germany 34132;Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany 39016
Venue:
Numerical Algorithms
Year:
2012

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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驴驴驴2 living on the refined mesh and discontinuous, piecewise polynomial projection spaces of order less than or equal to r驴驴驴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.