Discrete harmonics for stream function-vorticity Stokes problem
Numerical Analysis
2024-12-16 v1 Numerical Analysis
Abstract
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order one for the L2 norm of the vorticity.
Cite
@article{arxiv.2412.09996,
title = {Discrete harmonics for stream function-vorticity Stokes problem},
author = {François Dubois and Michel Salaün and Stéphanie Salmon},
journal= {arXiv preprint arXiv:2412.09996},
year = {2024}
}