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arXiv · 2301.01818

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

Mark Ainsworth·Charles Parker
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Abstract

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.

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Mark Ainsworth, Charles Parker. 2023-01-04. Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow. https://arxiv.org/abs/2301.01818

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