SIAM Journal on Numerical Analysis, Volume 59, Issue 2, Page 1090-1116, January 2021.
We construct and analyze an isoparametric finite element pair for the Stokes problem in two dimensions. The pair is defined by mapping the Scott--Vogelius finite element space via a Piola transform. The velocity space has the same degrees of freedom as the quadratic Lagrange finite element space, and therefore the proposed spaces reduce to the Scott--Vogelius pair in the interior of the domain. We prove that the resulting method converges with optimal order, is divergence-free, and is pressure-robust. Numerical examples are provided which support the theoretical results.

中文翻译：

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弯曲域上的无散度Scott-Vogelius元素

SIAM数值分析杂志，第59卷，第2期，第1090-1116页，2021年1月。
我们为二维Stokes问题构造并分析了等参有限元对。该对通过通过Piola变换映射Scott-Vogelius有限元素空间来定义。速度空间具有与二次Lagrange有限元空间相同的自由度，因此拟议的空间在域内部简化为Scott-Vogelius对。我们证明了所得方法收敛于最优阶，无散度，并且耐压。提供了数值示例，以支持理论结果。