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We propose an efficient variant of a primal Discontinuous Galerkin method with interior penalty for the second order elliptic equations on very general meshes (polytopes with eventually curved boundaries). Efficiency, especially when higher order polynomials are used, is achieved by static condensation, i.e. a local elimination of certain degrees of freedom element by element. This alters the original method in a way that preserves the optimal error estimates. Numerical experiments confirm that the solutions produced by the new method are indeed very close to that produced by the classical one.

A primal discontinuous Galerkin method with static condensation on very general meshes