A grad-div stabilized projection finite element method for a double-diffusive natural convection model

A Modular Grad-Div Stabilization Method for Time-Dependent Thermally Coupled MHD Equations

“…For the time-dependent Stokes/Darcy model, two grad-div stabilization methods were proposed in [ 20 ]. In addition, a grad-div stabilized projection finite-element method for a double-diffusive natural convection model was given in [ 21 ]. In view of this, a great deal of related interesting works have been reported in the recent years [ 22 , 23 , 24 ].…”

Deferred defect‐correction finite element method for the Darcy‐Brinkman model

“…Due to important applications, this model has been widely employed in industry and engineering [7][8][9]. At the time of writing, there are some works devoted to the development of efficient numerical methods for the problem (1) (see [10][11][12][13][14][15][16][17] and the references therein). Applying the Fourier-Galerkin spectral method, Shao et al [18] have obtained a high-accurate reference solution for the double-diffusive convection in a confined saturated porous medium.…”

Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model

“…Numerical methods of Navier-Stokes/Darcy have attracted a lot of attention. So far, a great deal of numerical methods are proposed to solve this model by virtue of different ways, such as finite element methods [12], discontinuous Galerkin finite element methods [5], two-grid methods [1,15,16], modified two-grid methods [6], partitioned time stepping method [7], characteristic stabilized finite element methods [8], mortar finite element methods [2], grad-div stabilized projection finite element method [14], modular grad-div method [11] and so on. The grad-div stabilized method is first introduced in [4], which can penalize mass conservation and improve the solution quality efficiently.…”