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A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model

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Abstract

In this paper, we study numerical methods for a coupled Stokes-Darcy model. This model is composed by Stokes equations in the fluid domain and Darcy’s law in the porous media domain, coupling together through certain interface conditions. By introducing a Lagrange multiplier, the coupled model is formed into a saddle point problem. A nonconforming mixed finite element method with nonmatching meshes is proposed to solve this coupled problem. The well-posedness of the discrete problem is proved. Moreover, we derive the a priori error estimates of the proposed finite element method. Numerical examples are also given to confirm the theoretical results.

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Acknowledgements

We would like to thank the anonymous referees who made many helpful comments and suggestions. This work was supported by NSFC under the grant 11071124 and 10871100. M. Cai’s work was supported in part by DFG through the grant SFB708.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Peiqi Huang

  2. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, People’s Republic of China

    Jinru Chen

  3. Department of Mathematics, Worcester Polytechnique Institute, Worcester, MA, 01609, USA

    Mingchao Cai

Authors
  1. Peiqi Huang
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  2. Jinru Chen
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  3. Mingchao Cai
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Correspondence to Jinru Chen.

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Huang, P., Chen, J. & Cai, M. A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model. J Sci Comput 53, 377–394 (2012). https://doi.org/10.1007/s10915-012-9574-y

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  • DOI: https://doi.org/10.1007/s10915-012-9574-y

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