319 IGPM319.pdf        June 2011
TITLE On the Accuracy of the Level Set SUPG Method for Approximating Interfaces
AUTHORS Arnold Reusken, Eva Loch
ABSTRACT In this paper we consider a level set equation, the solution of which (called level set function) is used to capture a moving interface denoted by Γ. We assume that this level set function is close to a signed distance function. For discretization of the linear hyperbolic level set equation we use standard polynomial finite element spaces with SUPG stabilization combined with a Crank- Nicolson time differencing scheme. Recently, in [Burmann, Comp. Methods Appl. Mech. Eng. 199, 2010] a discretization error bound for this discretization has been derived. The discretization induces an approximate interface, denoted by Γh. Using the discretization error bound, we derive bounds on the distance between Γ and its approximation Γh. From this we deduce a quantitative result on the mass conservation quality of the evolving approximate interface Γh. Results of numerical experiments are included which illustrate the theoretical error bounds.
KEYWORDS finite element, streamline diffusion stabilization, streamline-upwind Petrov-Galerkin, level set method, mass conservation