TY - JOUR
T1 - Optimal and Pressure-Independent $L^2$ Velocity Error Estimates for a Modified Crouzeix-Raviart Stokes Element with BDM Reconstructions
AU - Brennecke , C.
AU - Linke , A.
AU - Merdon , C.
AU - Schöberl , J.
JO - Journal of Computational Mathematics
VL - 2
SP - 191
EP - 208
PY - 2015
DA - 2015/04
SN - 33
DO - http://doi.org/10.4208/jcm.1411-m4499
UR - https://global-sci.org/intro/article_detail/jcm/9836.html
KW - Variational crime, Crouzeix-Raviart finite element, Divergence-free mixed method, Incompressible Navier-Stokes equations, A priori error estimates.
AB - <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>