@Article{JCM-33-2,
author = {C., Brennecke and Linke, A. and Merdon, C. and Schöberl, J.},
title = {Optimal and Pressure-Independent $L^2$ Velocity Error Estimates for a Modified Crouzeix-Raviart Stokes Element with BDM Reconstructions},
journal = {Journal of Computational Mathematics},
year = {2015},
volume = {33},
number = {2},
pages = {191--208},
abstract = {<p style="text-align: justify;">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 $H^1$ 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 $L^2$ velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1411-m4499},
url = {https://global-sci.com/article/84594/optimal-and-pressure-independent-l2-velocity-error-estimates-for-a-modified-crouzeix-raviart-stokes-element-with-bdm-reconstructions}
}