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A multilevel Monte Carlo finite element method for the stochastic Cahn-Hilliard-Cook equation. (English) Zbl 1465.76076

Summary: In this paper, we employ the multilevel Monte Carlo finite element method to solve the stochastic Cahn-Hilliard-Cook equation. The Ciarlet-Raviart mixed finite element method is applied to solve the fourth-order equation. In order to estimate the mild solution, we use finite elements for space discretization and the semi-implicit Euler-Maruyama method in time. For the stochastic scheme, we use the multilevel method to decrease the computational cost (compared to the Monte Carlo method). We implement the method to solve three specific numerical examples (both two- and three dimensional) and study the effect of different noise measures.

MSC:

76M35 Stochastic analysis applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
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