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ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099
Indexed in
EFFICIENT NUMERICAL METHODS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS THROUGH TRANSFORMATION TO EQUATIONS DRIVEN BY CORRELATED NOISE
Краткое описание
A procedure is provided for the efficient approximation of solutions of a broad class of stochastic partial differential equations (SPDEs), that is, partial differential equations driven by additive white noise. The first step is to transform the given SPDE into an equivalent SPDE driven by a correlated random process, specifically, the Ornstein-Uhlenbeck process. This allows for the use of truncated Karhunen-Loeve expansions and sparse-grid methods for the efficient and accurate approximation of the input stochastic process in terms of few random variables. Details of the procedure are given and its efficacy is demonstrated through computational experiments involving the stochastic heat equation and the stochastic Navier-Stokes equations.
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Aretaki Aikaterini, Karatzas Efthymios N., Random geometries for optimal control PDE problems based on fictitious domain FEMs and cut elements, Journal of Computational and Applied Mathematics, 412, 2022. Crossref
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Li Chen, Qin Ruibin, Ming Ju, Wang Zhongming, A discontinuous Galerkin method for stochastic Cahn–Hilliard equations, Computers & Mathematics with Applications, 75, 6, 2018. Crossref