A Stochastic Collocation Method based on Sparse Grids for a Stochastic Stokes-Darcy Model
In this paper, we develop a sparse grid stochastic collocation method to improve the computational efficiency in handling the steady Stokes-Darcy model with random hydraulic conductivity. To represent the random hydraulic conductivity, the truncated Karhunen-Loève expansion is used. For the discrete form in probability space, we adopt the stochastic collocation method and then use the Smolyak sparse grid method to improve the efficiency. For the uncoupled deterministic subproblems at collocation nodes, we apply the general coupled finite element method. Numerical experiment results are presented to illustrate the features of this method, such as the sample size, convergence, and randomness transmission through the interface.
Z. Yang et al., "A Stochastic Collocation Method based on Sparse Grids for a Stochastic Stokes-Darcy Model," Discrete and Continuous Dynamical Systems - Series S, vol. 15, no. 4, pp. 893 - 912, American Institute of Mathematical Sciences (AIMS), Apr 2022.
The definitive version is available at https://doi.org/10.3934/dcdss.2021104
Mathematics and Statistics
Keywords and Phrases
Finite Elements; Karhunen-Loève Expansion; Sparse Grid; Stochastic Collocation Method; Stochastic Partial Differential Equation; Stokes-Darcy Flow
International Standard Serial Number (ISSN)
Article - Journal
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01 Apr 2022