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Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II


Verfürth, R (1991). Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II. Numerische Mathematik, 59(6):615-636.

Abstract

We consider mixed finite element approximations of the stationary, incompressible Navier-Stokes equations with slip boundary condition simultaneously approximating the velocity, pressure, and normal stress component. The stability of the schemes is achieved by adding suitable, consistent penalty terms corresponding to the normal stress component and to the pressure. A new method of proving the stability of the discretizations allows, us to obtain optimal error estimates for the velocity, pressure, and normal stress component in natural norms without using duality arguments and without imposing uniformity conditions on the finite element partition. The schemes can easily be implemented into existing finite element codes for the Navier-Stokes equations with standard Dirichlet boundary conditions.

We consider mixed finite element approximations of the stationary, incompressible Navier-Stokes equations with slip boundary condition simultaneously approximating the velocity, pressure, and normal stress component. The stability of the schemes is achieved by adding suitable, consistent penalty terms corresponding to the normal stress component and to the pressure. A new method of proving the stability of the discretizations allows, us to obtain optimal error estimates for the velocity, pressure, and normal stress component in natural norms without using duality arguments and without imposing uniformity conditions on the finite element partition. The schemes can easily be implemented into existing finite element codes for the Navier-Stokes equations with standard Dirichlet boundary conditions.

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22 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1991
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:29
Publisher:Springer
ISSN:0029-599X
Free access at:Related URL. An embargo period may apply.
Publisher DOI:10.1007/BF01385799
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN362160546_0059&DMDID=dmdlog38

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