A Narrow Band Finite Element Method for the Level Set Equation

SIAM Journal on Scientific Computing, vol. 47, pp. A762–A789

Abstract

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 [Formula: see text]- or [Formula: see text]-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 backward difference formula 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.

Authors 2

1. Maxim A. Olshanskii

   University of Houston

   Affiliation as printed

   Department of Mathematics, University of Houston, Houston, TX 77204-3008 USA

2. Arnold Reusken Aachen Institute for Geometry and Applied Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Applied Mathematics, RWTH-Aachen University, D-52056 Aachen, Germany