We introduce and analyze a Statically Condensed Iterated Penalty (SCIP) method for solving incompressible flow problems discretized with $p$th-order Scott-Vogelius elements. While the standard iterated penalty method is often the preferred algorithm for computing the discrete solution, it requires inverting a linear system with $\mathcal{O}(p^{d})$ unknowns at each iteration. The SCIP method reduces the size of this system to $\mathcal{O}(p^{d-1})$ unknowns while maintaining the geometric rate of convergence of the iterated penalty method. The application of SCIP to Kovasznay flow and Moffatt eddies shows good agreement with the theory.

翻译：我们引入并分析一种用标准迭代处罚法(SCIP)解决与Scott-Vogelius元素分解的不压缩流动问题的方法。标准迭代处罚法通常是计算离散溶液的首选算法,但它要求每次迭代时用$\mathcal{O}(p ⁇ d})美元来颠倒线性系统。 SCIP法将这一系统的规模降低到$\mathcal{O}(p ⁇ d-1})美元,同时保持迭代处罚方法汇合的几何率。 SCIP对 Kovasznay 流和 Moffatt eddies 的应用与理论相当一致。