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.

翻译：本文研究不可压缩流体在流函数-涡量形式下的二维斯托克斯问题。针对该问题，经典一阶有限元方法在涡量L2范数意义下仅能达到二分之一阶收敛精度。我们提出采用调和函数逼近边界处的涡量分布。离散调和函数作为实际计算工具，可用于推导新的数值方法。我们证明，该数值格式在涡量L2范数意义下能达到一阶误差精度。