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

Authors:
Peiqi Huang;Jinru Chen;Mingchao Cai
Affiliations:
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, People's Republic of China 210037;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, People's Republic of China 210046;Department of Mathematics, Worcester Polytechnique Institute, Worcester, USA 01609
Venue:
Journal of Scientific Computing
Year:
2012

Citing 12
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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.