000180349 001__ 180349
000180349 005__ 20190316235443.0
000180349 0247_ $$2doi$$a10.1002/nme.2656
000180349 022__ $$a0029-5981
000180349 037__ $$aARTICLE
000180349 245__ $$aAnalysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
000180349 269__ $$a2009
000180349 260__ $$c2009
000180349 336__ $$aJournal Articles
000180349 520__ $$aWe consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochastic coefficients of the PDE are approximated by truncated Karhunen–Loève expansions driven by a finite number of uncorrelated random variables. After approximating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE of the same type, the dimension of the parameter set being equal to the number of random variables introduced. After proving that the solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based on tensor product, total degree or sparse polynomial spaces and constructed by either a Stochastic Galerkin or a Stochastic Collocation approach. We derive convergence rates for the different cases and present numerical results that show how these approaches are a valid alternative to the more traditional Monte Carlo Method for this class of problems. Copyright © 2009 John Wiley & Sons, Ltd.
000180349 6531_ $$aPDEs with random data
000180349 6531_ $$aparabolic equations
000180349 6531_ $$amultivariate polynomial approximation
000180349 6531_ $$aStochastic Galerkin methods
000180349 6531_ $$aStochastic Collocation methods
000180349 6531_ $$asparse grids
000180349 6531_ $$aSmolyak approximation
000180349 6531_ $$aPoint Collocation
000180349 6531_ $$aMonte Carlo sampling
000180349 700__ $$0241873$$g118353$$aNobile, Fabio
000180349 700__ $$aTempone, Raul
000180349 773__ $$j80$$tINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING$$k6-7$$q979-1006
000180349 8564_ $$uhttps://infoscience.epfl.ch/record/180349/files/Analysis_and_implementation_issues.pdf$$zn/a$$s344800$$yn/a
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000180349 937__ $$aEPFL-ARTICLE-180349
000180349 973__ $$rNON-REVIEWED$$sPUBLISHED$$aOTHER
000180349 980__ $$aARTICLE