The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter epsilon > 0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order O(epsilon2) are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)-solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.
Sharp error analysis for curvature dependent evolving fronts / R.H. Nochetto, M. Paolini, C. Verdi. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 3:6(1993), pp. 711-723. [10.1142/S0218202593000369]
Sharp error analysis for curvature dependent evolving fronts
C. VerdiUltimo
1993
Abstract
The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter epsilon > 0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order O(epsilon2) are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)-solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.
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