Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model

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• 作者：Tong Zhang ; Jiaojiao Jin
• 关键词：Stokes equations ; Darcy’s law ; multimodeling problems ; decoupled scheme
• 刊名：Advances in Difference Equations
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1618KB
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847
• 卷排序：2017

文摘

This paper considers two kinds of novel decoupled algorithms for the non-stationary Stokes-Darcy model. In this way, the considered problem is decoupled into one time-dependent Stokes equations and one linear parabolic equation. For the two algorithms, we establish the stability and the optimal error estimates. Furthermore, the existing result in Mu and Zhu (Math. Comput. 79:707-731, 2010) can be improved to the optimal order \(\mathcal{O}(\Delta t)\) following our proof. Finally, some numerical experiments are conducted to validate the established theoretical results.