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Computational Mechanics

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26-04-2023 | Letter

On the space discretization and time integration for level set convection

Authors: Ze Zhao, Jinhui Yan

Published in: Computational Mechanics | Issue 6/2023

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Abstract

One canonical practice in the development and application of level set methods is to convect a shape represented by zero level set with a given, reversible, and periodic velocity field and test how well the original shape is recovered after each cycle. In this short letter, we mathematically show that Crank–Nicolson time integration, combined with standard Galerkin finite element, can exactly recover the original shape after each cycle, regardless of spatiotemporal resolution. This surprising finding is also numerically demonstrated by LeVeque’s problem.

next article A simple geometrically exact finite element for thin shells—Part 1: statics

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Title: On the space discretization and time integration for level set convection
Authors: Ze Zhao
Jinhui Yan
Publication date: 26-04-2023
Publisher: Springer Berlin Heidelberg
Published in: Computational Mechanics / Issue 6/2023
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-023-02338-3

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