Spectral stochastic two‐scale convergence method for parabolic PDEs | Zendy

Jardak M. | Zendy; Navon I. M. | Zendy

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Spectral stochastic two‐scale convergence method for parabolic PDEs

Author(s) -

Jardak M.,

Navon I. M.

Publication year - 2010

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.2997

Subject(s) - mathematics , convergence (economics) , scale (ratio) , partial differential equation , parabolic partial differential equation , gaussian , stochastic process , spectral method , stochastic differential equation , mathematical analysis , statistical physics , physics , statistics , quantum mechanics , economics , economic growth

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 σ ε ( t, x , ω) of the form σ( t, x, t/ ε γ , 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.

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