A Class Of Stable Hybrid Discontinuous Finite Element Method

Discontinuous Galerkin Method keeps many advantages of classical finite element methods. Totally discontinuous elements are used in the approximation scheme, which enables DG methods to capture high oscillations or variations in boundary layers. Some DG methods, such as LDG method, can be solved symbolly, and have nice stabilization.In this thesis a mixed finite element discretization is considered for Passion equation with dirichlet boundary condition. and new formulation for the stabilization was introduced. Instead of using a jump of solution or its gradient as it was usually done we use residual stabilization. The boundedness, stability and consistency are presented. And the basic error estimates are obtained with respect to the defined norm.