Finite Element Methods for Coupled Stokes and Darcy Problems |
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Authors: | LIANG Tao FENG Min-fu QI Rui-sheng |
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Affiliation: | 1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China 2. Department of Mathematics, Sichuan University, Chengdu 610064, China |
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Abstract: | We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H(div) conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H(div) finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation. |
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Keywords: | Finite element method Mass conservation Beavers-Joseph-Saffman condition Stockes and Darcy problems |
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