A priori error analysis of discrete-ordinate weak Galerkin method for radiative transfer equation

This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-discrete hyperbolic system is approximated using the weak Galerkin method. The stability result for the proposed numerical method is devised. A \emph{priori} error analysis is established under the suitable norm. In order to examine the theoretical results, numerical experiments are carried out

A weak galerkin finite element method for singularly perturbed convection-diffusion–reaction problems

In this article, a new weak Galerkin finite element method is introduced to solve convection-diffusion–reaction equations in the convection dominated regime. Our method is highly flexible by allowing the use of discontinuous approximating functions on polytopal mesh without imposing extra conditions on the convection coefficient. An error estimate is devised in a suitable norm. Numerical examples are provided to confirm theoretical findings and efficiency of the method