We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity form. The classical finite element method of degree one usually used does not allow the vorticity on the boundary of the domain to be computed satisfactorily when the meshes are unstructured and does not converge optimally. To better approach the vorticity along the boundary, we propose that harmonic functions obtained by integral representation be used. Numerical results are very satisfactory, and we prove that this new numerical scheme leads to an optimal convergence rate of order 1 for the natural norm of the vorticity and, under higher regularity assumptions, from 3/2 to 2 for the quadratic norm of the vorticity.
Publié le : 2004-07-05
Classification:
Stokes problem,
stream function-vorticity formulation,
harmonic functions,
integral representation,
65N30 76D07 76M10,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00085271,
author = {Abboud, Toufic and Sala\"un, Michel and Salmon, St\'ephanie},
title = {Coupling harmonic functions-finite elements for solving stream function-vorticity Stokes problem},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00085271}
}
Abboud, Toufic; Salaün, Michel; Salmon, Stéphanie. Coupling harmonic functions-finite elements for solving stream function-vorticity Stokes problem. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00085271/