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Numerical analysis of the stochastic Stokes equations of Wick type
Author(s) -
Manouzi H.,
Theting T.G.
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20166
Subject(s) - mathematics , uniqueness , type (biology) , partial differential equation , finite element method , set (abstract data type) , numerical analysis , stochastic differential equation , stokes problem , stochastic partial differential equation , mathematical analysis , computer science , ecology , physics , biology , programming language , thermodynamics
We propose a finite element method for the numerical solution of the stochastic Stokes equations of the Wick type. We give existence and uniqueness results for the continuous problem and its approximation. Optimal error estimates are derived and algorithmic aspects of the method are discussed. Our method will reduce the problem of solving stochastic Stokes equations to solving a set of deterministic ones. Moreover, one can reconstruct particular realizations of the solution directly from Wiener chaos expansions once the coefficients are available. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007