Year: 2017
Author: Peiqi Huang, Jinru Chen, Mingchao Cai
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 3 : pp. 596–620
Abstract
In this work, we study numerical methods for a coupled fluid-porous media flow model. The model consists of Stokes equations and Darcy's equations in two neighboring subdomains, coupling together through certain interface conditions. The weak form for the coupled model is of saddle point type. A mortar finite element method is proposed to approximate the weak form of the coupled problem. In our method, nonconforming Crouzeix-Raviart elements are applied in the fluid subdomain and the lowest order Raviart-Thomas elements are applied in the porous media subdomain; meshes in different subdomains are allowed to be nonmatching on the common interface; interface conditions are weakly imposed via adding constraint in the definition of the finite element space. The well-posedness of the discrete problem and the optimal error estimate for the proposed method are established. Numerical experiments are also given to confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2016.m1397
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 3 : pp. 596–620
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Mortar method nonconforming element mixed element inf-sup condition Stokes equations Darcy's equations error estimate.
Author Details
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Mortar Element Method for the Time Dependent Coupling of Stokes and Darcy Flows
Chen, Yanping
Zhao, Xin
Huang, Yunqing
Journal of Scientific Computing, Vol. 80 (2019), Iss. 2 P.1310
https://doi.org/10.1007/s10915-019-00977-4 [Citations: 5]