A comparison between weak form meshless local Petrov-Galerkin method (MLPG) and strong form meshless diffuse approximate method (DAM) is performed for the diffusion equation in two dimensions. The shape functions are in both methods obtained by moving least squares (MLS) approximation with the polynomial weight function of the fourth order on the local support domain with 13 closest nodes. The ...

In the earlier paper [6] a Galerkin method was proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary value problem of the form U = F ( ; U). This was converted to a problem on a standard domain and then converted to an equivalent integral equation. Galerkin’s method was used to solve the integral equation, with the eigenfunctions of the Lapl...

We present a robust posteriori error estimator for weak Galerkin finite element method applied to stationary convection-diffusion equations in the convection-dominated regime. The provides global upper and lower bounds of is sense that are uniformly bounded with respect diffusion coefficient. we use was developed by Lin, Ye, Zhang, Zhu (2018) problem without assuming any additional conditions o...

A simplified primal-dual weak Galerkin (S-PDWG) finite element method is designed for the Fokker–Planck-type equation with nonsmooth diffusion tensor and drift vector. The discrete system resulting from S-PDWG has significantly fewer degrees of freedom compared one PDWG proposed by Wang-Wang. Furthermore, condition number smaller than (Wang-Wang) due to introduction a new stabilizer, which prov...

In this paper, the global nonlinear Galerkin method is used to perform an accurate and efficient analysis of the large deflection behavior of a simplysupported rectangular plate under combined loads. Through applying the Galerkin method to the governing nonlinear partial differential equations (PDEs) of the plate, we derive a system of coupled third order nonlinear algebraic equations (NAEs). H...

In this paper we present an analysis of three di erent formulations of the discontinuous Galerkin method for di usion equations. The rst formulation yields an inconsistent and weakly unstable scheme, while the other two formulations, the local discontinuous Galerkin approach and the Baumann-Oden approach, give stable and convergent results. When written as nite di erence schemes, such a distinc...