Kornhuber, R. and Schwab, C. and Wolf, M.W. (2014) Multilevel Monte Carlo finite element methods for stochastic elliptic variational inequalities. SIAM Journal on Numerical Analysis, 52 (3). pp. 12431268. ISSN 00361429

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Official URL: http://dx.doi.org/10.1137/130916126
Abstract
Multilevel Monte Carlo finite element methods (MLMCFEMs) 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 optimalorder error estimates of the statistical error and upper bounds for the corresponding computational cost for the classical MC method and novel MLMCFEMs. Utilizing suitable multigrid solvers for the occurring sample problems, in two space dimensions MLMCFEMs 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.
Item Type:  Article 

Uncontrolled Keywords:  multilevel Monte Carlo, stochastic partial differential equations, stochastic finite element methods, multilevel methods, variational inequalities 
Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1788 
Deposited By:  Ekaterina Engel 
Deposited On:  17 Feb 2016 09:32 
Last Modified:  03 Mar 2017 14:41 
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