Open AccessCoupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem
Author(s) -
Toufic Abboud,
Michel Salaün,
Stéphanie Salmon
Publication year - 2004
Publication title -
hal (le centre pour la communication scientifique directe)
Language(s) - English
DOI - 10.1002/num.2005
Subject(s) - stream function , vorticity , coupling (piping) , function (biology) , harmonic , physics , mathematical analysis , mathematics , classical mechanics , mechanics , vortex , acoustics , engineering , mechanical engineering , evolutionary biology , biology
International audienceWe consider the bidimensional Stokes problem for incompressible uids in stream function-vorticity form. The classical nite 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