Geodesic
Worst scenario method in homogenization. Linear case
Applications of Mathematics, Tome 51 (2006) no. 3, pp. 263-294 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 of generalized gradient in the places where these components change and on the average of homogenized solution in some critical subdomain.
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 of generalized gradient in the places where these components change and on the average of homogenized solution in some critical subdomain.
DOI : 10.1007/s10492-006-0015-9
Classification : 35B27, 35B40, 35J25, 35R05, 49J20
Keywords: homogenization; two-scale convergence; worst-scenario; reliable solution 
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     title = {Worst scenario method in homogenization. {Linear} case},
     journal = {Applications of Mathematics},
     pages = {263--294},
     year = {2006},
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Nechvátal, Luděk. Worst scenario method in homogenization. Linear case. Applications of Mathematics, Tome 51 (2006) no. 3, pp. 263-294. doi: 10.1007/s10492-006-0015-9

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