A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes

A new discontinuous Galerkin finite element method for the Stokes equations is developed in primary velocity-pressure formulation. This employs polynomials both velocity and pressure on general polygonal/polyhedral meshes. Most methods with approximation have one or more stabilizing terms to guarantee stability convergence. has standard conforming formulation, without any stabilizers. Optimal-order error estimates are established corresponding numerical various norms. The examples tested low high order elements up degree four 2D 3D spaces.