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Publications in Scientific Journals:

C. Brennecke, A. Linke, C. Merdon, J. Schöberl:
"Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM";
Journal of Computational Mathematics, 33 (2015), 2; 191 - 208.



English abstract:
Abstract
Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a priori estimates for the velocity error become pressure-dependent, while divergence-free mixed finite elements deliver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas velocity reconstructions delivers a much more robust modified Crouzeix-Raviart element, obeying an optimal pressure-independent discrete H velocity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure-independent L velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.

Keywords:
Variational crime, Crouzeix-Raviart finite element, Divergence-free mixed method, Incompressible Navier-Stokes equations, A priori error estimates.


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.4208/jcm.1411-m4499

Electronic version of the publication:
http://publik.tuwien.ac.at/files/PubDat_246131.docx


Created from the Publication Database of the Vienna University of Technology.