We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits in two dimensions. The velocity space simply consists of continuous, piecewise linear polynomials, where as the pressure space is a subspace of piecewise constants with weak continuity properties at singular edges (3D) and singular vertices (2D). We discuss implementation aspects that arise when coding the pressure space, and in particular, show that the pressure constraints can be enforced at an algebraic level.

翻译：我们利用Workery-Farin在三个维度上分裂和鲍威尔-萨宾在两个维度上分裂,得出斯托克斯问题的低顺序、内向稳定、无差异的有限元素近似值。 速度空间只是由连续的、片断的线性多面空间组成, 压力空间是单边缘( 3D) 和单脊椎(2D) 中具有薄弱连续性的片断常数的子空间。 我们讨论了压力空间编码时产生的执行方面, 特别是显示压力限制可以在代数水平上实施。