Finite element approximation of level set motion by powers of the mean curvature

Abstract : In this paper we study the level set formulations of certain geometric evolution equations from a numerical point of view. Specifically, we consider the flow by powers greater than one of the mean curvature and the inverse mean curvature flow. Since the corresponding equations in level set form are quasilinear, degenerate and especially possibly singular a regularization method is used in the literature to approximate these equations to overcome the singularities of the equations. Motivated by the paper [29] which studies the finite element approximation of inverse mean curvature flow we prove error estimates for the finite element approximation of the regularized equations for the flow by powers of the mean curvature. We validate the rates with numerical examples. Additionally, the regularization error in the rotational symmetric case for both flows is analyzed numerically. All calculations are performed in the 2D case.
Complete list of metadatas

Cited literature [55 references]  Display  Hide  Download

https://hal-ensta-paris.archives-ouvertes.fr//hal-01138347
Contributor : Axel Kröner <>
Submitted on : Tuesday, April 24, 2018 - 10:00:54 PM
Last modification on : Tuesday, October 1, 2019 - 1:32:17 AM

File

KKK.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01138347, version 2

Citation

Axel Kröner, Eva Kröner, Heiko Kröner. Finite element approximation of level set motion by powers of the mean curvature . [Research Report] INRIA Saclay. 2015. ⟨hal-01138347v2⟩

Share

Metrics

Record views

541

Files downloads

259