Preprint 1998-026

Relaxation Schemes for Curvature-Dependent Front Propagation

Shi Jin, Markos Katsoulakis, and Zhouping Xin

Abstract: In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature dependent local law. In the Chapman-Enskog expansion, this relaxation approximation leads to the level set equation for transport dominated front propagation, that includes the mean curvature as the next order term. This approach yields a new and possibly attractive way of calculating numerically the propagation of curvature dependent fronts. Since the relaxation system is a symmetrizable, semilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature-dependent front propagation, without discretizing directly the complicated, yet singular, mean curvature term.

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Relaxation schemes for curvature-dependent front propagation
Shi Jin, <>
Markos Katsoulakis
Zhouping Xin
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<> July 27 1998.

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