The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary conditions a challenging problem. A very popular strategy is to rely on the so-called Nitsche method~[22]. We show with numerically examples that in some degenerate trimmed domain configurations there is a lack of stability of the formulation, potentially polluting the computed solutions. After extending the stabilization procedure of~[16] to incompressible flow problems, we theoretically prove that, combined with the Raviart-Thomas, the N\'ed\'elec, and the Taylor-Hood (in this case, only when the isogeometric map is the identity) isogeometric elements, we are able to recover the well-posedness of the formulation and, consequently, optimal a priori error estimates. Numerical results corroborating the theory are provided.

翻译：正在研究修剪版面 Stokes 问题的等离子度近似值。 这一环境的特点是与物理版面的边界格格格格格不入,使强加基本边界条件成为具有挑战性的问题。 一个非常受欢迎的战略是依赖所谓的Nitsche 方法~[ 22]。 我们用数字实例显示,在一些变形的缩略角域配置中,配方缺乏稳定性,可能污染计算出来的解决方案。在将~[16] 的稳定程序延伸至无法压缩的流程问题之后,我们在理论上证明,与Raviart-Thomas、N\'ed\'elec和Taylor-Hood(在此情况下,只有当等离子图是身份)等分数要素一起,我们能够恢复配方的精度,因此也能够最佳的先验误算结果。提供了证实理论的数值结果。