180349
20190316235443.0
doi
10.1002/nme.2656
0029-5981
ARTICLE
Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
2009
2009
Journal Articles
We consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochastic coefficients of the PDE are approximated by truncated Karhunen–Loève expansions driven by a finite number of uncorrelated random variables. After approximating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE of the same type, the dimension of the parameter set being equal to the number of random variables introduced. After proving that the solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based on tensor product, total degree or sparse polynomial spaces and constructed by either a Stochastic Galerkin or a Stochastic Collocation approach. We derive convergence rates for the different cases and present numerical results that show how these approaches are a valid alternative to the more traditional Monte Carlo Method for this class of problems. Copyright © 2009 John Wiley & Sons, Ltd.
PDEs with random data
parabolic equations
multivariate polynomial approximation
Stochastic Galerkin methods
Stochastic Collocation methods
sparse grids
Smolyak approximation
Point Collocation
Monte Carlo sampling
241873
Nobile, Fabio
118353
Tempone, Raul
80
6-7
979-1006
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
344800
http://infoscience.epfl.ch/record/180349/files/Analysis_and_implementation_issues.pdf
n/a
n/a
252411
CSQI
U12495
oai:infoscience.tind.io:180349
SB
article
GLOBAL_SET
178574
EPFL-ARTICLE-180349
OTHER
NON-REVIEWED
PUBLISHED
ARTICLE