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Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

Part of: Partial differential equations, boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  27 January 2016

Jing Zhao  and
Tong Zhang
Jing Zhao*
Affiliation:
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003, P.R. China and Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Curitiba 81531-980, P.R. Brazil
Tong Zhang
Affiliation:
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003, P.R. China and Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Curitiba 81531-980, P.R. Brazil
*
*Corresponding author. Email addresses:zhaojing0216@163.com (J. Zhao), tzhang@hpu.edu.cn (T. Zhang)
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Abstract

Two-grid finite element methods for the steady Navier-Stokes/Darcy model are considered. Stability and optimal error estimates in the H1-norm for velocity and piezometric approximations and the L2-norm for pressure are established under mesh sizes satisfying h = H2. A modified decoupled and linearised two-grid algorithm is developed, together with some associated optimal error estimates. Our method and results extend and improve an earlier investigation, and some numerical computations illustrate the efficiency and effectiveness of the new algorithm.

Keywords

Navier-Stokes equationsDarcy's lawmultimodeling problemstwo-grid method

MSC classification

Secondary: 65N15: Error bounds 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 76D07: Stokes and related (Oseen, etc.) flows
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 1 , February 2016 , pp. 60 - 79
Copyright
Copyright © Global-Science Press 2016 

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