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.

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.

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

C. Verdi
Ultimo
1995

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.
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/178598
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