# American Institute of Mathematical Sciences

May  2014, 19(3): 849-865. doi: 10.3934/dcdsb.2014.19.849

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

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

Received  September 2013 Revised  November 2013 Published  February 2014

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.
Citation: Tong Zhang, Jinyun Yuan. Two novel decoupling algorithms for the steady Stokes-Darcy model based on two-grid discretizations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 849-865. doi: 10.3934/dcdsb.2014.19.849
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