Double obstacle formulation with variable relaxation parameter for smooth geometric front evolutions: asymptotic interface error estimates

Maurizio Paolini, R. H. Nochetto, C. Verdi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

A singularly perturbed double obstacle problem is examined as a variational tool for the approximation of the geometric motion of fronts. The relaxation parameter is space-time dependent, thereby allowing the control of transition layer thickness and related interface pointwise accuracy. Optimal order interface error estimates are derived for smooth evolutions. The estimates have a local character for small time, namely they depend on the relaxation parameter local magnitude. The proof is based on constructing suitable sub and supersolutions, which incorporate a number of shape corrections to the basic standing wave profile, and using a modified distance function to the front. Numerical simulations illustrate how the variable transition layer thickness can be exploited in dealing with large curvatures and ultimately in resolving singularities.
Original languageEnglish
Pages (from-to)173-198
Number of pages26
JournalAsymptotic Analysis
Publication statusPublished - 1995

Keywords

  • Allen-Cahn equation
  • mean curvature flow

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