Two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations

Tong Zhang; Jinyun Yuan

doi:10.3934/dcdsb.2014.19.849

Article Contents

2014, Volume 19, Issue 3: 849-865. Doi: 10.3934/dcdsb.2014.19.849

This issue Previous Article The second-order two-scale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials Next Article

Two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations

Tong Zhang^1, and
Jinyun Yuan^2,

1.
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo, 454003
2.
Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Curitiba 81531-980

Received: September 2013

Revised: November 2013

Published: May 2014

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Abstract

In this work, two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations are proposed and analyzed. Optimal error estimates for these variables are presented. Two grid decoupled scheme proposed by Mu and Xu (2007) is used to develop the two novel decoupling algorithms. For Algorithm 3.2, the optimal error estimates are obtained for both ${\bf{u}}_f,\ p_f$ and $\phi$ with mesh sizes satisfying $H=\sqrt{h}$. For Algorithm 3.3, the convergence of $\phi$ in $H^1$-norm is improved form $H^2$ to $H^\frac{5}{2}$. Furthermore, the existing results in [17] are improved and supplemented. Finally, some numerical experiments are provided to show the efficiency and effectiveness of the developed algorithms.

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Mathematics Subject Classification: Primary: 65N15, 65N30; Secondary: 76D07.

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