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): doi: /
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

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): doi: /
Figure Legend:
Realizations of the response field for example 1

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): doi: /
Figure Legend:
10,000 realizations of the random response process for example 2

4. 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): doi: /
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)

5. 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): doi: /
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))

6. 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): doi: /
Figure Legend:
(a) Expected value of the random response; (b) relative error in expected value

7. 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): doi: /
Figure Legend:
(a) Covariance function h(x)=Covu(x,(Ly/2),x,(Ly/2)); (b) relative error in covariance

8. 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): doi: /
Figure Legend:
(a) Histograms and (b) cumulative probability distribution of random variable u(x*,y*,ω)

9. 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): doi: /
Figure Legend:
(a) Expected value of the random response; (b) relative error in expected value

10. 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): doi: /
Figure Legend:
(a) Covariance function h=h(x); (b) relative error in covariance approximation

11. 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): doi: /
Figure Legend:
(a) Histograms and (b) cumulative probability distribution of random variable u(x*,y*,ω)