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New decoupled method for the evolutionary dual-porosity-Stokes model with Beavers-Joseph interface conditions. (English) Zbl 1484.65210

Summary: In this paper, we present and analyze a decoupled method for the nonstationary dual-porosity-Stokes coupling problem with the Beavers-Joseph interface conditions. Instead of solving the whole coupling problem on each time step, the proposed scheme allows the coupling problem to be divided into four subproblems in a non-iterative manner, which improves the computational efficiency. Specifically, a Stokes subproblem on a half-time step is calculated first, by using its solution as the interface information, we solve uncoupled matrix pressure equation, microfracture pressure equation and Stokes equation separately. The stability analysis and error estimation of the decoupled algorithm are presented. They show that if the rescaling factor is small enough, our scheme is stable on a bounded time interval and optimal convergent. The reliability of the theoretical analysis and the feasibility of the scheme are verified by the numerical experiments.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows

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