Abstract
<abstract> A new conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the Stokes equations. The CDG method gets its name by combining good features of both conforming finite element method and discontinuous finite element method. It has the flexibility of using discontinuous approximation and simplicity in formulation of the conforming finite element method. This new CDG method is not only stabilizer free but also has two order higher convergence rate than the optimal order. This CDG method uses discontinuous $ P_k $ element for velocity and continuous $ P_{k+1} $ element for pressure. Order two superconvergence is derived for velocity in an energy norm and the $ L^2 $ norm. The superconvergent $ P_k $ solution is lifted elementwise to a $ P_{k+2} $ velocity which converges at the optimal order. The numerical experiments confirm the theories. </abstract>
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