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A second‐order partitioned method with different subdomain time steps for the evolutionary Stokes‐Darcy system
Author(s) -
Li Yi,
Hou Yanren
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4744
Subject(s) - mathematics , discretization , extrapolation , stability (learning theory) , mathematical optimization , order (exchange) , algorithm , mathematical analysis , computer science , finance , machine learning , economics
A second‐order decoupled algorithm for the nonstationary Stokes‐Darcy system, which allows different time steps in two subregions, is proposed and analyzed in this paper. The algorithm, which is a combination of the second‐order backward differentiation formula and second‐order extrapolation method, uncouples the problem into two decoupled problems per time step. We prove the unconditional stability and long‐time stability of the decoupled scheme with different time steps and derive error estimates of this decoupled algorithm using finite element spatial discretization. Numerical experiments are provided to illustrate the accuracy, effectiveness, and stability of the decoupled algorithm and show its advantages of increasing accuracy and efficiency.