Electron. J. Differential Equations, Vol. 2017 (2017), No. 24, pp. 1-10.

A stabilized finite element method for Stream function vorticity formulation of Navier-Stokes equations

Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine

Abstract:
We the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numerical algorithm is presented and tested.

Submitted October 29, 2016. Published January 19, 2017.
Math Subject Classifications: 35D30, 76D03, 65N30.
Key Words: Stream function; vorticity; stabilized method, high performance computing.

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Mohamed Abdelwahed
Department of Mathematics, College of Sciences
King Saud University
Riyadh, Saudi Arabia
email: mabdelwahed@ksu.edu.sa
Nejmeddine Chorfi
Department of Mathematics, College of Sciences
King Saud University
Riyadh, Saudi Arabia
email: nchorfi@ksu.edu.sa
Maatoug Hassine
Department of Mathematics, College of Sciences
Monastir University, Tunisia
email: maatoug_hassine@yahoo.fr

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