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We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients.
The Wiener-Askey polynomial chaos for stochastic differential equations
Dongbin Xiu and George Em Karniadakis · 2002
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Crossover from nonlinearity controlled to heterogeneity controlled mixing in two-phase porous media flows
Frederico Furtado and Felipe Pereira · 2003
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Galerkin finite element approximations of stochastic elliptic partial differential equations
Ivo Babuška, Raúl Tempone, and Georgios E. Zouraris · 2004
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Finite elements for elliptic problems with stochastic coefficients
Philipp Frauenfelder, Christoph Schwab, and Radu Alexandru Todor · 2005
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Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
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Regularity results for the ordinary product stochastic pressure equation
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Sparse polynomial approximation of parametric elliptic pdes. part i: affine coefficients
Markus Bachmayr, Albert Cohen, and Giovanni Migliorati · 2017
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