A STOCHASTIC COLLOCATION METHOD based on SPARSE GRIDS for a STOCHASTIC STOKES-DARCY MODEL

Abstract

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.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS-1722647

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)

1937-1179; 1937-1632

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Apr 2022

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