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Abstract
We consider the bi-dimensional Stokes problem for incompressible fluids in the stream function-vorticity formulation. For this problem, the classical finite-element method of degree one converges with an order of only 1/2 for the quadratic norm of the error on the vorticity. We propose changing the method of approximation and adding harmonic functions to approach vorticity along the boundary. The numerical results are very satisfactory and we prove that this new numerical scheme leads to an error of order 1 for the natural norm of the vorticity and under more regularity assumptions from 3/2 to 2 for the quadratic norm of the vorticity.
This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.