Statically condensed iterated penalty method for high order finite element discretizations of incompressible flow

We introduce and analyze a statically condensed iterated penalty (SCIP) method for solving incompressible flow problems discretized with pth 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 O(pd) unknowns at each iteration. The SCIP method reduces the size of this system to 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.