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Numerical analysis for the mixed N avier– S tokes and D arcy Problem with the B eavers– J oseph interface condition
Author(s) -
Zuo Liyun,
Hou Yanren
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21933
Subject(s) - uniqueness , grid , finite element method , mathematics , scheme (mathematics) , partial differential equation , interface (matter) , mathematical analysis , physics , geometry , mechanics , bubble , maximum bubble pressure method , thermodynamics
In this article, we consider the coupled Navier–Stokes and Darcy problem with the Beavers–Joseph interface condition. With suitable restrictions of physical parameters α and ν , we prove the existence and local uniqueness of a weak solution. Then we propose a coupled finite element scheme and a decoupled and linearized scheme based on two‐grid finite element. Under suitable further restrictions, their optimal error estimates are obtained. Finally numerical experiments indicate the validity of the theoretical results as well as the efficiency and effectiveness of the decoupled and linearized two‐grid algorithm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1009–1030, 2015