A conforming discontinuous Galerkin finite element method on rectangular partitions

<p style='text-indent:20px;'>This article presents a conforming discontinuous Galerkin (conforming DG) scheme for second order elliptic equations on rectangular partitions. The new method is based DG finite element space and uses weak gradient arising from local Raviart Thomas approximations. By using the enforcing inter-element continuity strongly, maintains simple formulation of while have flexibility Hence, programming complexity this significantly reduced compared to other existing methods. Error estimates optimal are established corresponding approximations in various discrete Sobolev norms. Numerical results presented confirm developed convergence theory.</p>