Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs
Foundations of Computational Mathematics
Sparse Tensor Discretization of Elliptic sPDEs
SIAM Journal on Scientific Computing
Editorial: High-order finite element approximation for partial differential equations
Computers & Mathematics with Applications
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In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane C^N. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.