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RWTH Publication No: 47338 2011 IGPM319.pdf 
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,
streamlineupwind PetrovGalerkin,
level set method, mass conservation
