[2211.07012] Phi-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations
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Mathematics > Numerical Analysis

arXiv:2211.07012 (math)
[Submitted on 13 Nov 2022 (v1), last revised 27 Jan 2023 (this version, v2)]

Title:Phi-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

Authors:Michel Duprez, Vanessa Lleras, Alexei Lozinski
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Abstract:We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H1 norm for the velocity and L2 for pressure; numerically also in the L2 norm for the velocity).
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N30, 65N85, 65N15
Cite as: arXiv:2211.07012 [math.NA]
  (or arXiv:2211.07012v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.07012

Submission history

From: Michel Duprez Mr [view email]
[v1] Sun, 13 Nov 2022 20:35:34 UTC (1,666 KB)
[v2] Fri, 27 Jan 2023 14:37:16 UTC (1,671 KB)
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