Displaying similar documents to “Inverse problems in spaces of measures”

Total overlapping Schwarz' preconditioners for elliptic problems

Faker Ben Belgacem, Nabil Gmati, Faten Jelassi (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem , 336 (2003) 277–282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the behavior of the solution at infinity, when...

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

Filippo Cagnetti, Rodica Toader (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to...

Image segmentation with a finite element method

Blaise Bourdin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on -convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete...