Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations (Communications in Computational Physics, 2025)
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 ofweak solutions. The discretization of domain is accomplished using a triangularmesh, with the lowest order Raviart-Thomas element utilized for Darcy equations andBernardi-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 inapproximating solutions.
Keywords: Darcy equations; Navier-Stokes equations; coupling; finite elements; mortar.