Microelectronic devices with multifunctional capabilities have become an indispensable part
of the modern life. These devices generate significant thermal energy during continuous use …

This article is assigned to the numerical analysis of a new weak Galerkin mixed-type finite
element method for the diffusion-convection-reaction problem with singular perturbation …

Abstract The Cahn-Hilliard phase-field model of two-phase incompressible flows, namely
the Cahn-Hilliard-Navier-Stokes (CH-NS) problem represents the fundamental building …

This paper proposes and analyzes a weak Galerkin (WG) finite element method for 2-and 3-
dimensional convection–diffusion–reaction problems on conforming or nonconforming …

In this short paper, we introduce an efficient finite element method for solving the Stokes
equations based on a divergence free H (div) element. The strong curl of C 0-P k+ 1 basis …

The present article introduces, mathematically analyzes, and numerically validates a new
weak Galerkin mixed finite element method based on Banach spaces for the stationary …

A robust residual-based a posteriori error estimator is proposed for a weak Galerkin finite
element method for the Stokes problem in two and three dimensions. The estimator consists …

In this paper, we consider a weak Galerkin finite element method for the Kelvin-Voigt
viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to …

In this paper, a fully discrete weak Galerkin (WG) finite element method is proposed to solve
Biot's consolidation problem, where weakly defined gradient and divergence operators over …

We add new inter-element variables to the BDM H (div) finite elements on triangular and
tetrahedral meshes for the Stokes equations. With the weak gradient, we enforce weakly the …