A conforming discontinuous Galerkin finite element method
For researchers in numerical PDEs, this method offers a new hybrid approach that simplifies DG formulations while retaining flexibility, though it is an incremental contribution building on existing DG and conforming methods.
This paper introduces a conforming discontinuous Galerkin (DG) finite element method for second-order elliptic problems, combining the flexibility of discontinuous approximations with the simplicity of conforming methods. Optimal-order error estimates are established in discrete H1 and L2 norms, supported by numerical results.
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method, we call it conforming DG method. While using DG finite element space, this conforming DG method maintains the features of the conforming finite element method such as simple formulation and strong enforcement of boundary condition. Therefore, this finite element method has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. Error estimates of optimal order are established for the corresponding discontinuous finite element approximation in both a discrete $H^1$ norm and the $L^2$ norm. Numerical results are presented to confirm the theory.