Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities
Metadata only
Datum
2014Typ
- Journal Article
Abstract
Multilevel Monte Carlo finite element methods (MLMC-FEMs) for the solution of stochastic elliptic variational inequalities are introduced, analyzed, and numerically investigated. Under suitable assumptions on the random diffusion coefficient, the random forcing function, and the deterministic obstacle, we prove existence and uniqueness of solutions of “pathwise” weak formulations. Suitable regularity results for deterministic, elliptic obstacle problems lead to uniform pathwise error bounds, providing optimal-order error estimates of the statistical error and upper bounds for the corresponding computational cost for the classical MC method and novel MLMC-FEMs. Utilizing suitable multigrid solvers for the occurring sample problems, in two space dimensions MLMC-FEMs then provide numerical approximations of the expectation of the random solution with the same order of efficiency as for a corresponding deterministic problem, up to logarithmic terms. Our theoretical findings are illustrated by numerical experiments. Mehr anzeigen
Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SIAM Journal on Numerical AnalysisBand
Seiten / Artikelnummer
Verlag
SIAMThema
Multilevel Monte Carlo; Stochastic partial differential equations; Stochastic finite element methods; Multilevel methods; Variational inequalitiesOrganisationseinheit
03435 - Schwab, Christoph / Schwab, Christoph
Förderung
247277 - Automated Urban Parking and Driving (EC)
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Is new version of: https://doi.org/10.3929/ethz-a-010391178