On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties
Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 439–458
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-940
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 4 : pp. 439–458
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: nonconforming finite elements Korn's inequality Stokes equations error estimates.