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Mathematics > Numerical Analysis

arXiv:2407.02950 (math)
[Submitted on 3 Jul 2024]

Title:A narrow band finite element method for the level set equation

Authors:Maxim Olshanskii, Arnold Reusken, Paul Schwering
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Abstract:A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band around the interface. An extension procedure, which is essential for a narrow band level set method, is introduced based on a finite element $L^2$- or $H^1$-projection combined with the ghost-penalty method. This procedure is formulated as a linear variational problem in a narrow band around the surface, making it computationally efficient and suitable for rigorous error analysis. The extension method is combined with a discontinuous Galerkin space discretization and a BDF time-stepping scheme. The paper analyzes the stability and accuracy of the extension procedure and evaluates the performance of the resulting narrow band finite element method for the level set equation through numerical experiments.
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:2407.02950 [math.NA]
  (or arXiv:2407.02950v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2407.02950

Submission history

From: Maxim Olshanskii [view email]
[v1] Wed, 3 Jul 2024 09:37:05 UTC (4,605 KB)
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