An Efficient Ensemble Algorithm for Numerical Approximation of Stochastic Stokes–Darcy Equations


We propose and analyze an efficient ensemble algorithm for fast computation of multiple realizations of the stochastic Stokes-Darcy model with a random hydraulic conductivity tensor. The algorithm results in a common coefficient matrix for all realizations at each time step making solving the linear systems much less expensive while maintaining comparable accuracy to traditional methods that compute each realization separately. Moreover, it decouples the Stokes–Darcy system into two smaller sub-physics problems, which reduces the size of the linear systems and allows parallel computation of the two sub-physics problems. We prove the ensemble method is long time stable and first-order in time convergent under a time-step condition and two parameter conditions. Numerical examples are presented to support the theoretical results and illustrate the application of the algorithm.


Mathematics and Statistics


The first author was partially supported by the US National Science Foundation grant DMS-1720001 and a University of Missouri Research Board grant. The second author was partially supported by the US National Science Foundation grant DMS-1720001.

Keywords and Phrases

Ensemble algorithm; Finite element method; Partitioned method; Stokes-Darcy equations; Uncertainty quantification

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Article - Journal

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© 2019 Elsevier B.V., All rights reserved.

Publication Date

01 Jan 2019