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Quasi-Monte Carlo finite element methods for elliptic PDEs with log-normal random coefficient
(2013)SAM Research ReportIn this paper we analyze the numerical approximation of diffusion problems over polyhedral domains in $R^d$ (d=1,2,3), with diffusion coefficient a(x,ω) given as a lognormal random field, i.e., a(x,ω)=exp(Z(x,ω)) where x is the spatial variable and Z(x,⋅) is a Gaussian random field. The analysis presents particular challenges since the corresponding bilinear form is not uniformly bounded away from 0 or ∞ over all possible realizations of ...Report