We consider the approximation of curvature dependent geometric front evolutions by singularly perturbed parabolic double obstacle problems with small parameter epsilon. We give a simplified proof of optimal interface error estimates of order O(epsilon2), valid in the smooth regime, which is based on constructing precise barriers, perturbing the forcing term and exploiting the maximum principle.
Quadratic rate of convergence for curvature dependent smooth interfaces: a simple proof / R.H. Nochetto, M. Paolini, C. Verdi. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - 7:4(1994 Jul), pp. 59-63.
Quadratic rate of convergence for curvature dependent smooth interfaces: a simple proof
C. VerdiUltimo
1994
Abstract
We consider the approximation of curvature dependent geometric front evolutions by singularly perturbed parabolic double obstacle problems with small parameter epsilon. We give a simplified proof of optimal interface error estimates of order O(epsilon2), valid in the smooth regime, which is based on constructing precise barriers, perturbing the forcing term and exploiting the maximum principle.
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