A variational formulation is analysed for the Oseen equations written in terms of vorticity 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 Nédélec finite elements and piecewise continuous polynomials for the vorticity and the Bernoulli pressure, respectively. The a priori error analysis is carried out in the L2-norm for vorticity, pressure, and velocity; under a smallness assumption either on the convecting velocity, or on the mesh parameter. Furthermore, an 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 also confirm the theoretical findings.

中文翻译：

---

Oseen 方程的涡量/伯努利压力公式的误差分析

对用涡量和伯努利压力编写的 Oseen 方程的变分公式进行了分析。速度使用动量平衡方程完全解耦，然后通过后处理恢复。还提出了一种有限元方法，分别由涡度和伯努利压力的等阶 Nédélec 有限元和分段连续多项式组成。这先验误差分析在L中进行2- 涡量、压力和速度的标准；在对流速度或网格参数的小假设下。此外，一个后验的设计了误差估计器，并使用加权规范研究了它的鲁棒性和效率。最后，给出了一组 2D 和 3D 数值示例，其中误差指示器用于指导自适应网格细化。这些测试说明了新配方在典型流动条件下的行为，也证实了理论发现。