Approximations of effective coefficients in stochastic homogenization

By A. Bourgeat, Andrey L. Piatnitski. 2002

202 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/bf56df3c5772fa52778146d4aebaf13df5972cce

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Variance decay for functionals of the environment viewed by the particle (2009, methodology): “Considering divergence form elliptic operators and using results from [27], it is shown in [4] that Dn(ω) converges to D faster than Cn−α , where α depends on the dimension d ≥ 3, the ellipticity constant and some mixing condition.”
Numerical Study of Two-grid Preconditioners for 1-d Elliptic Problems with Highly Oscillating Discontinuous Coefficients (2007, unknown): “, [11] and [2]).”
Quantitative stochastic homogenization of convex integral functionals (2014, result): “Otto [19], Conlon and Spencer [7] as well as earlier works of Yurinskii [28], Naddaf and Spencer [24], Bourgeat and Piatnitski [6] and Boivin [5].”
Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media (2005, result): “We also refer to [ BP ] for other more recent results in the”
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications (2005, unknown): “We also refer to Bourgeat and Piatniski [6] for som recent results in the linear case as well as more references.”
Reduction of the resonance error---Part 1: Approximation of homogenized coefficients (2011, background): “13), which is self-contained, sligthly departs from the approach by Bourgeat & Piatnitski in [4].”
Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics (2013, background): “For a discussion of the literature on error estimates for the approximation of homogenized coefficients (and in particular [42], [6], and [13]), we refer the reader to [23, Section 1.”
Adaptive finite element heterogeneous multiscale method for homogenization problems (2011, methodology): “The modeling error estimates from [16] or [25, Theorem 2.”