A variational formulation is introduced for the Oseen equations written in terms of vor\-ti\-city and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A finite element method is also proposed, consisting in equal-order N\'ed\'elec finite elements and piecewise continuous polynomials for the vorticity and the Bernoulli pressure, respectively. The {\it a priori} error analysis is carried out in the $\mathrm{L}^2$-norm for vorticity, pressure, and velocity; under a smallness assumption either on the convecting velocity, or on the mesh parameter. Furthermore, an {\it a posteriori} error estimator is designed and its robustness and efficiency are studied using weighted norms. Finally, a set of numerical examples in 2D and 3D is given, where the error indicator serves to guide adaptive mesh refinement. These tests illustrate the behaviour of the new formulation in typical flow conditions, and they also confirm the theoretical findings.

翻译：对以vor\-ti\-city-city和Bernoulli 压力写成的 Oseen 方程式采用了一种变式配方。速度完全脱钩,使用动向平衡方程式,然后通过后处理加以恢复。还提出了一种有限元素方法,包括等序 N\'ed\'elec 限定元素和小曲连续的多元体,分别用于园艺和Bernoulli 压力。在色素、压力和速度方面,进行了一个先验的错误分析;在小数假设下,或者放在凝固速度上,或者放在网状参数上。此外,用加权规范设计了一个后继误差估计器,并研究了其坚固性和效率。最后,在 2D 和 3D 中提供了一套数字示例,其中的误差指标用来指导调适的调和微。这些测试显示了新配方在典型流动条件下的行为,它们还证实了理论结论。