Reduced Basis Techniques for Stochastic Problems

Sébastien Boyaval

doi:10.1007/s11831-010-9056-z

Reduced Basis Techniques for Stochastic Problems

2010-10-16

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DOI：10.1007/s11831-010-9056-z

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We report here on the recent application of a now classical general reduction technique, the Reduced-Basis (RB) approach initiated by C. Prud'homme et al. in J. Fluids Eng. 124(1), 70-80, 2002, to the specific context of differential equations with random coefficients. After an elementary presentation of the approach, we review two contributions of the authors: in Comput. Methods Appl. Mech. Eng. 198(41-44), 3187-3206, 2009, which presents the application of the RB approach for the discretization of a simple second order elliptic equation supplied with a random boundary condition, and in Commun. Math. Sci., 2009, which uses a RB type approach to reduce the variance in the Monte-Carlo simulation of a stochastic differential equation. We conclude the review with some general comments and also discuss possible tracks for further research in the direction.

Keyword:

PARTIAL-DIFFERENTIAL-EQUATIONS

POSTERIORI ERROR ESTIMATION

SOLID MECHANICS HELD

BASIS APPROXIMATION

FUNCTIONAL QUANTIZATION

VARIANCE REDUCTION

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Reduced Basis Techniques for Stochastic Problems

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