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A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods

✍ Scribed by Maxim A. Olshanskii

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
365 KB
Volume
191
Category
Article
ISSN
0045-7825

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✦ Synopsis

A Galerkin finite element method is considered to approximate the incompressible Navier-Stokes equations together with iterative methods to solve a resulting system of algebraic equations. This system couples velocity and pressure unknowns, thus requiring a special technique for handling. We consider the Navier-Stokes equations in velocity-kinematic pressure variables as well as in velocity--Bernoulli pressure variables. The latter leads to the rotation form of nonlinear terms. This form of the equations plays an important role in our studies. A consistent stabilization method is considered from a new view point. Theory and numerical results in the paper address both the accuracy of the discrete solutions and the effectiveness of solvers and a mutual interplay between these issues when particular stabilization techniques are applied.

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