Preprint 1998-026

Relaxation Schemes for Curvature-Dependent Front Propagation

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.

Paper:

Available as PostScript.

Title:

Relaxation schemes for curvature-dependent front propagation

Author(s):

Shi Jin, <jin@math.gatech.edu>

Markos Katsoulakis

Zhouping Xin

Publishing information:

Comments:

Submitted by:

<jin@math.gatech.edu> July 27 1998.