×

On homogenization of elliptic equations with random coefficients. (English) Zbl 0956.35013

The authors investigate the rate of convergence of the solutions \(u_\varepsilon\) of the random elliptic partial difference equation \[ (\nabla^{\varepsilon*}a(x/\varepsilon,\omega)\nabla^\varepsilon+1) u_\varepsilon(x,\omega)=f(x) \] to the corresponding homogenized solution. Here \(x\in \varepsilon\mathbb Z^d\), and \(\omega \in \Omega\) represents the randomness. Under some conditions an upper bound \(\varepsilon^\alpha\) for the rate of convergence is established with a constant \(\alpha\) which depends on \(d\) and the deviation of \(a(x,\omega)\) from the identity matrix.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35R60 PDEs with randomness, stochastic partial differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML EMIS