@Article{CiCP-37-3,
author = {Zhao, Xin and Chuanjun, Chen},
title = {Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations},
journal = {Communications in Computational Physics},
year = {2025},
volume = {37},
number = {3},
pages = {701--739},
abstract = {<p style="text-align: justify;">The article discusses a nonlinear system that is dependent on time and coupled by incompressible fluid and porous media flow. Treating Darcy flow as dual-mixed form, we propose a variational formulation and prove the well-posedness of
weak solutions. The discretization of domain is accomplished using a triangular
mesh, with the lowest order Raviart-Thomas element utilized for Darcy equations and
Bernardi-Raugel element used for Navier-Stokes equations. Using the mortar method,
we construct the spaces from which numerical solutions are sought. Based on backward Euler method, we establish a fully discrete algorithm. At each single time level,
the first-order convergence is demonstrated through the use of the Gronwall inequality. Numerical experiments are provided to illustrate the algorithm’s effectiveness in
approximating solutions.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0009},
url = {https://global-sci.com/article/91729/mortar-finite-element-method-for-the-coupling-of-time-dependent-navier-stokes-and-darcy-equations}
}