A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms (Advances in Applied Mathematics and Mechanics, 2022)
A conforming discontinuous Galerkin finite element method was introducedby Ye and Zhang, on simplicial meshes and on polytopal meshes, which has the flexibility of using discontinuous approximation and an ultra simple formulation. Themain goal of this paper is to improve the above discontinuous Galerkin finite elementmethod so that it can handle nonhomogeneous Dirichlet boundary conditions effectively. In addition, the method has been generalized in terms of approximation of theweak gradient. 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.