The minimization of the functional G(v)=H(S v)+∫ ∂Ω m·v-∫ Ω k·v is related to various geometrical type problems in calculus of variations, such as the minimal partition of a set, the segmentation of images, and the search for sets with prescribed curvature. The functional G is first regularized and next discretized by means of piecewise linear finite elements with numerical quadratures, thus allowing its actual minimization on a computer. The discrete functionals converge to G in the sense of Γ-convergence, which implies the convergence of the discrete minima to a minimum of G. Various numerical experiments illustrate the behaviour of the numerical algorithm.
Numerical minimization of geometrical type problems related to calculus of variations / G. Bellettini, M. Paolini, C. Verdi. - In: CALCOLO. - ISSN 0008-0624. - 27:3-4(1990), pp. 251-278.
Titolo: | Numerical minimization of geometrical type problems related to calculus of variations |
Autori: | VERDI, CLAUDIO (Ultimo) |
Parole Chiave: | AMS(MOS) subject classifications (1985 revision): 53A10, 65K10, 65N30 |
Settore Scientifico Disciplinare: | Settore MAT/08 - Analisi Numerica |
Data di pubblicazione: | 1990 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/BF02575797 |
Appare nelle tipologie: | 01 - Articolo su periodico |