Homogenization with uncertain input parameters

Luděk Nechvátal

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Displaying similar documents to “Homogenization with uncertain input parameters”

Worst scenario method in homogenization. Linear case

Luděk Nechvátal (2006)

Applications of Mathematics

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The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values...

Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity

Niklas Wellander (2002)

Applications of Mathematics

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The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of...

Homogenization of variational problems in manifold valued Sobolev spaces

Jean-François Babadjian, Vincent Millot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna [ (1999) 185–206]. For energies with superlinear or linear growth, a -convergence result is established in Sobolev spaces, the homogenization problem in the space of functions of bounded variation being the object of...

The method of Rothe and two-scale convergence in nonlinear problems

Jiří Vala (2003)

Applications of Mathematics

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Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.