TY - JOUR
T1 - A Discontinuous Galerkin Finite Element Method Without Interior Penalty Terms
AU - Gao , Fuzheng
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 299
EP - 314
PY - 2022
DA - 2022/01
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2020-0247
UR - https://global-sci.org/intro/article_detail/aamm/20199.html
KW - Nonhomogeneous Dirichlet boundary conditions, weak gradient, discontinuous
Galerkin, stabilizer, penalty free, finite element methods, polytopal mesh.
AB - <p style="text-align: justify;">A conforming discontinuous Galerkin finite element method was introduced
by Ye and Zhang, on simplicial meshes and on polytopal meshes, which has the flexibility of using discontinuous approximation and an ultra simple formulation. The
main goal of this paper is to improve the above discontinuous Galerkin finite element
method so that it can handle nonhomogeneous Dirichlet boundary conditions effectively. In addition, the method has been generalized in terms of approximation of the
weak 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.</p>