A two-level local projection stabilisation on uniformly refined triangular meshes
- 122 Downloads
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.
KeywordsStabilised finite elements Local projection stabilisation
Mathematics Subject Classifications (2010)65N12 65N30 65N15
Unable to display preview. Download preview PDF.
- 5.Ern, A., Guermond, J.-L.: Theory and practice of finite elements. Applied Mathematical Sciences, vol. 159. Springer-Verlag, New York (2004)Google Scholar
- 11.Lube, G.: Stabilized FEM for incompressible flow. Critical review and new trends. In: Wesseling P., Onate E., Périaux J. (eds.) European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006, pp. 1–20. TU Delft, The Netherlands (2006)Google Scholar
- 14.Roos, H.-G., Stynes, M., Tobiska, L.: Robust numerical methods for singularly perturbed differential equations. Convection-diffusion-reaction and flow problems. Springer Series in Computational Mathematics, vol. 24. Springer-Verlag, Berlin (2008)Google Scholar
- 15.Tobiska, L.: Recent results on local projection stabilization for convection-diffusion and flow problems. In: Hegarty A., Kopteva N., O’Riordan E., Stynes M. (eds.) BAIL 2008 – Boundary and Interior Layers, no. 69 in LNCSE, pp. 55–75. Springer (2009)Google Scholar