Zurück zu den Preprints des Jahres 2011


2011-29

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

by Matthies, G., Tobiska, L..


Series: 2011-29, Preprints

MSC:
65N12 Stability and convergence of numerical methods
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds

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 $r\ge 2$ 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

This paper was published in:
Numerical Algorithm