TY - JOUR
T1 - On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties
AU - P. Knobloch & L. Tobiska
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 439
EP - 458
PY - 2005
DA - 2005/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/940.html
KW - nonconforming finite elements, Korn's inequality, Stokes equations, error estimates.
AB - <p style="text-align: justify;">We investigate the Korn first inequality for quadrilateral
nonconforming finite elements of first order approximation properties
and clarify the dependence of the constant in this inequality on the
discretization parameter $h$. Then we use the nonconforming elements for
approximating the velocity in a discretization of the Stokes equations
with boundary conditions involving surface forces and, using the result
on the Korn inequality, we prove error estimates which are optimal for
the pressure and suboptimal for the velocity.</p>