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. [10.1007/BF02575797]

Numerical minimization of geometrical type problems related to calculus of variations

C. Verdi
Ultimo
1990

Abstract

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.
AMS(MOS) subject classifications (1985 revision): 53A10, 65K10, 65N30
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/2434/187409
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