A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model

A Mortar Method Using Nonconforming and Mixed Finite Elements for the Coupled Stokes-Darcy Model

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

Peiqi Huang

Jinru Chen

Mingchao Cai

  1. 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]