Volume 9, Issue 3
A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model

Adv. Appl. Math. Mech., 9 (2017), pp. 596-620.

Published online: 2018-05

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• 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.

65N12, 65N30, 65N55, 76D07, 76S05

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@Article{AAMM-9-596, author = {Huang , PeiqiChen , Jinru and Cai , Mingchao}, title = {A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1397}, url = {http://global-sci.org/intro/article_detail/aamm/12166.html} }
TY - JOUR T1 - A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model AU - Huang , Peiqi AU - Chen , Jinru AU - Cai , Mingchao JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 596 EP - 620 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2016.m1397 UR - https://global-sci.org/intro/article_detail/aamm/12166.html KW - Mortar method, nonconforming element, mixed element, inf-sup condition, Stokes equations, Darcy's equations, error estimate. AB -

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.

Peiqi Huang, Jinru Chen & Mingchao Cai. (2020). A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model. Advances in Applied Mathematics and Mechanics. 9 (3). 596-620. doi:10.4208/aamm.2016.m1397
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