SIAM Journal on Numerical Analysis, Volume 59, Issue 3, Page 1245-1272, January 2021.
This paper is the second part in a series on a mass conserving, high order, mixed finite element method for Stokes flow. In this part, we construct optimal $hp$-approximations for two classes of functions: (1) functions with general Sobolev regularity which lead to algebraic convergence rates using locally quasi-uniform meshes, and (2) singular functions belonging to countably normed (weighted) spaces which lead to exponential convergence using geometrically graded meshes. In turn, the finite element spaces we considered in part I [M. Ainsworth and C. Parker, SIAM J. Numer. Anal., 59 (2021), pp. 1218--1244] have optimal convergence properties, which is demonstrated by two numerical examples: Moffatt eddies in a wedge and flow in a T-shaped cavity.

中文翻译：

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斯托克斯流量的质量守恒混合$ hp $ -FEM近似值。第二部分：最佳收敛

SIAM数值分析学报，第59卷，第3期，第1245-1272页，2021年1月。
本文是有关斯托克斯流的质量守恒，高阶混合有限元方法系列的第二部分。在本部分中，我们为两类函数构造最优的$ hp $逼近度：（1）具有一般Sobolev正则性的函数使用局部拟均匀网格导致代数收敛速度，以及（2）属于可数范数的奇异函数（加权）空间，这些空间会导致使用几何渐变网格进行指数收敛。反过来，我们在第一部分中考虑了有限元空间[M. Ainsworth和C.Parker，SIAM J.Numer。Anal。，59（2021），pp。1218--1244]具有最佳的收敛特性，这由两个数值示例证明：楔形的Moffatt涡和在T形腔中流动。