Spectral stochastic two‐scale convergence method for parabolic PDEs
Mohamed Jardak, Ionel Michael Navon · International Journal for Numerical Methods in Engineering · 2010
Abstract Following the theory of two‐scale convergence method introduced by Nguetseng (SIAM J. Math. Anal.1989;20:608–623) and further developed by Allaire (SIAM J. Math. Anal.1992;23:1482–1518), we introduce the chaos two‐scale method as a spectral stochastic tool to tackle parabolic partial differential equations where the material properties are stochastic processes σε(t, x, ω) of the form σ(t, x, t/εγ,x/ε, ω), oscillating in both space and time variables with different speeds. Periodicity with respect to the fast or local variables is assumed, and, stationary Gaussian material properties processes are considered. Copyright © 2010 John Wiley & Sons, Ltd.