A study of mixed problem for second order elliptic problems using modified weak Galerkin finite element method

Abstract

In this article, a modified weak Galerkin finite element method is developed for a second order elliptic problem with mixed boundary conditions. The basic idea of modified weak Galerkin method is to reduce the degrees of freedom in comparison to the standard weak Galerkin method. The optimal convergence orders in a discrete L2 norm and H1 norm are established. Numerical examples are presented to verify the theoretical estimates.