A system of diffusion–reaction equations coupled with a dissolution–precipitation model is discussed in this paper. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector results to justify the obtained theoretical results. Furthermore, we perform the numerical simulations to compare the outcome of the effective (homogenized) model with the original heterogeneous microscale model. [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]