[2301.01818] Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow
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Mathematics > Numerical Analysis

arXiv:2301.01818 (math)
[Submitted on 4 Jan 2023]

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

Authors: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.
Comments: 25 pages, 7 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 76M10, 65N30, 65N12
Cite as: arXiv:2301.01818 [math.NA]
  (or arXiv:2301.01818v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2301.01818

Submission history

From: Charles Parker [view email]
[v1] Wed, 4 Jan 2023 20:40:34 UTC (1,706 KB)
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