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Nonconforming Finite Element Method Applied to the Driven Cavity Problem

Part of: Numerical methods Partial differential equations, boundary value problems

Published online by Cambridge University Press:  08 March 2017

Roktaek Lim  and
Dongwoo Sheen
Roktaek Lim*
Affiliation:
Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
Dongwoo Sheen*
Affiliation:
Department of Mathematics, Seoul National University, Seoul 08826, Korea
*
*Corresponding author. Email addresses:rokt.lim@gmail.com (R. Lim), dongwoosheen@gmail.com (D. Sheen)
*Corresponding author. Email addresses:rokt.lim@gmail.com (R. Lim), dongwoosheen@gmail.com (D. Sheen)

Abstract

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A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P 1×P 0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

Keywords

Nonconforming finite element methodincompressible Navier-Stokes equationslid driven cavity problem

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 74S05: Finite element methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1012 - 1038
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Jie Shen

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