Volume 33, Issue 2
Optimal and Pressure-Independent L² Velocity Error Estimates for a Modified Crouzeix-Raviart Stokes Element with BDM Reconstructions

C. Brennecke ,  A. Linke ,  C. Merdon and J. Schöberl

10.4208/jcm.1411-m4499

J. Comp. Math., 33 (2015), pp. 191-208.

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  • 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 H¹ 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 L² velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.

  • History

Published online: 2015-04

  • AMS Subject Headings

65N30, 65N15, 76D07.

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