“…In this paper, we are concerned with the development of an SFWG finite element method using the following Poisson equation The standard weak Glaerkin (WG) method for the problem (1.1)-(1.2) seeks weak Galerkin finite element solution u h = {u 0 , u b } such that (∇ w u h , ∇ w v) + s(u h , v) = (f, v), (1.4) for all v = {v 0 , v b } with v b = 0 on ∂Ω, where ∇ w is the weak gradient operator and s(u h , v) in (1.4) is a stabilizer term that ensures a sufficient weak continuity for the numerical approximation. The WG method has been developed and applied to different types of problems, including convection-diffusion equations [7,6], Helmholtz equations [9,12,5], Stokes flow [11,10], and biharmonic problems [8]. Recently, Al-Taweel and Wang in [2], proposed the lowest-order weak Galerkin finite element method for solving reaction-diffusion equations with singular perturbations in 2D.…”