An assumed-gradient finite element method for the level set equation


Journal Article

The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton-Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd.

Full Text

Duke Authors

Cited Authors

  • Mourad, HM; Dolbow, J; Garikipati, K

Published Date

  • October 28, 2005

Published In

Volume / Issue

  • 64 / 8

Start / End Page

  • 1009 - 1032

International Standard Serial Number (ISSN)

  • 0029-5981

Digital Object Identifier (DOI)

  • 10.1002/nme.1395

Citation Source

  • Scopus