Brennecke, C., Linke, A., Merdon, C., & Schöberl, J. (2015). Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM. JOURNAL OF COMPUTATIONAL MATHEMATICS, 33(2), 191–208. https://doi.org/10.4208/jcm.1411-m4499
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.
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Research Areas:
Modelling and Simulation: 10% Computer Science Foundations: 20% Mathematical and Algorithmic Foundations: 70%
