Non-convergence result for conformal approximation of variational problems subject to a convexity constraint

Philippe Choné; Hervé V.J. Le Meur

doi:10.1081/NFA-100105306

Non-convergence result for conformal approximation of variational problems subject to a convexity constraint

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal P₁Finite Element sequence for a wide variety of refined meshes.

Original language	English
Pages (from-to)	529-547
Number of pages	19
Journal	Numerical Functional Analysis and Optimization
Volume	22
Issue number	5-6
DOIs	https://doi.org/10.1081/NFA-100105306
Publication status	Published - 1 Jan 2001
Externally published	Yes

Keywords

Conformal approximation
Convexity
Finite elements
Interpolation
Minimization

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10.1081/NFA-100105306

Cite this

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title = "Non-convergence result for conformal approximation of variational problems subject to a convexity constraint",

abstract = "In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal P1Finite Element sequence for a wide variety of refined meshes.",

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author = "Philippe Chon{\'e} and \{Le Meur\}, \{Herv{\'e} V.J.\}",

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AU - Choné, Philippe

AU - Le Meur, Hervé V.J.

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N2 - In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal P1Finite Element sequence for a wide variety of refined meshes.

AB - In this article, we are interested in the minimization of functionals in the set of convex functions. We investigate the discretization of the convexity through various numerical methods and find a geometrical obstruction confirmed by numerical simulations. We prove that there exist some convex functions that cannot be the limit of any conformal P1Finite Element sequence for a wide variety of refined meshes.

KW - Conformal approximation

KW - Convexity

KW - Finite elements

KW - Interpolation

KW - Minimization

U2 - 10.1081/NFA-100105306

DO - 10.1081/NFA-100105306

M3 - Article

AN - SCOPUS:0035416410

SN - 0163-0563

VL - 22

SP - 529

EP - 547

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 5-6

ER -

Non-convergence result for conformal approximation of variational problems subject to a convexity constraint

Abstract

Keywords

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