From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: Sparseness of the stiffness matrix of example 1: (a) for m = 4, n = 5, p = 1; (b) for m = 4, n = 140, p = 3

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: Realizations of the response field for example 1

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: 10,000 realizations of the random response process for example 2

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Convergence in expected value for u((Lx/2),(Ly/2),ω); (b) convergence in variance for u((Lx/2),(Ly/2),ω)

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Expected value of the response; (b) covariance function of the response process evaluated at (x,y*,t,y*)=(x,(Ly/2),t,(Ly/2))

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Expected value of the random response; (b) relative error in expected value

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Covariance function h(x)=Covu(x,(Ly/2),x,(Ly/2)); (b) relative error in covariance

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Histograms and (b) cumulative probability distribution of random variable u(x*,y*,ω)

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Expected value of the random response; (b) relative error in expected value

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Covariance function h=h(x); (b) relative error in covariance approximation

From: Galerkin Solution of Stochastic Reaction-Diffusion Problems Date of download: 11/1/2017 Copyright © ASME. All rights reserved. From: Galerkin Solution of Stochastic Reaction-Diffusion Problems J. Heat Transfer. 2013;135(7):071201-071201-12. doi:10.1115/1.4023938 Figure Legend: (a) Histograms and (b) cumulative probability distribution of random variable u(x*,y*,ω)