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Volume 2, Issue 4
On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties

P. Knobloch & L. Tobiska

Int. J. Numer. Anal. Mod., 2 (2005), pp. 439-458.

Published online: 2005-02

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  • 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.

  • Keywords

nonconforming finite elements, Korn's inequality, Stokes equations, error estimates.

  • AMS Subject Headings

65N12, 65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-439, author = {P. Knobloch and L. Tobiska}, title = {On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/940.html} }
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 -

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. Knobloch and L. Tobiska. (2005). On Korn's First Inequality for Quadrilateral Nonconforming Finite Elements of First Order Approximation Properties. International Journal of Numerical Analysis and Modeling. 2 (4). 439-458. doi:
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