Double obstacle formulation with variable relaxation parameter for smooth geometric front evolutions: asymptotic interface error estimates
Articolo
Data di Pubblicazione:
1995
Citazione:
Double obstacle formulation with variable relaxation parameter for smooth geometric front evolutions: asymptotic interface error estimates / R.H. Nochetto, M. Paolini, C. Verdi. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 10:2(1995), pp. 173-198. [10.3233/ASY-1995-10203]
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.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
R.H. Nochetto, M. Paolini, C. Verdi
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