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Mortar Element Method for the Time Dependent Coupling of Stokes and Darcy Flows

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Abstract

In this paper, we investigate a mortar element method for the time dependent coupling of incompressible flow and porous media flow which are governed by non-stationary Stokes and Darcy equations, respectively. The interface conditions are given by mass conservation, the balance of the normal forces and the Beavers–Joseph–Saffman law. We consider the dual-mixed formulation in Darcy region where velocity and pressure are both unknowns. We employ the lowest order Raviart–Thomas element for Darcy flow and choose Bernardi–Raugel element in the free fluid region. The backward Euler scheme is adopt to yield the fully discrete algorithm. At each single time step, we present a priori error estimate which shows the linear convergence. At the final, numerical experiments are provided to illustrate the performance of the developed algorithm that verify our analysis.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yanping Chen

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Xin Zhao

  3. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, China

    Yunqing Huang

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  1. Yanping Chen
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  2. Xin Zhao
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  3. Yunqing Huang
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Correspondence to Yanping Chen.

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This work is supported by National Natural Science Foundation of China (No. 11671157), National Natural Science Foundation of China Key Project (No. 91430213) and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2016B251, CX2017B266).

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Chen, Y., Zhao, X. & Huang, Y. Mortar Element Method for the Time Dependent Coupling of Stokes and Darcy Flows. J Sci Comput 80, 1310–1329 (2019). https://doi.org/10.1007/s10915-019-00977-4

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  • DOI: https://doi.org/10.1007/s10915-019-00977-4

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