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The lowest-order weak Galerkin finite element method is introduced and analysed for second order elliptic interface problems with discontinuous coefficients and solutions. Compared with the existing weak Galerkin finite element methods for interface problems, this method has a simpler formulation and superconvergence property. Hence it is suitable for more complicated interfaces and domain configurations. We derive the superconvergence error estimates in discrete H 1 and L 2 norms. Furthermore, we verify the theoretical results by numerical experiments. Optimal convergence rates are achieved for examples with low-regularity solutions. [ABSTRACT FROM AUTHOR]

A new conforming discontinuous Galerkin method, which is based on weak Galerkin finite element method, is introduced for solving second order elliptic interface problems with discontinuous coefficient. The numerical method studied in this paper has no stabilizer and fewer unknowns compared with the known weak Galerkin algorithms. The error estimates in H 1 and L 2 norms are established, which are the optimal order convergence. Numerical experiments demonstrate the performance of the method, confirm the theoretical results of accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we study a weak Galerkin (WG) finite element method for semiconductor device simulations. We consider the one-dimensional drift–diffusion (DD) and high-field (HF) models, which involves not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. The main difficulties in the analysis include the treatment of the nonlinearity and coupling of the models. The weak Galerkin finite element method adopts piecewise polynomials of degree k for the approximations of electron concentration and electric potential in the interior of elements, and piecewise polynomials of degree k + 1 for the discrete weak derivative space. The optimal order error estimates in a discrete H 1 norm and the standard L 2 norm are derived. Numerical experiments are presented to illustrate our theoretical analysis. Moreover, numerical schemes also work out for the discontinuous diffusion coefficient problems. [ABSTRACT FROM AUTHOR]