Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow

01/04/2023

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by   Mark Ainsworth, et al.

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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(p^d) 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.