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A Hybrid Discontinuous Galerkin Method for Elliptic Problems

A new family of hybrid discontinuous Galerkin methods is studied for second-order elliptic equations. Our proposed method is a generalization of the cell boundary element (CBE) method [Y. Jeon and E.-J. Park, Appl. Numer. Math., 58 (2008), pp. 800-814], which allows high order polynomial approximations. Our method can be viewed as a hybridizable discontinuous Galerkin method [B. Cockburn, J. Gopalakrishnan, and R. Lazarov, SIAM J. Numer. Anal., 47 (2009), pp. 1319-1365] using a Bauman-Oden-type local solver. The method conserves the mass in each element and the average flux is continuous across the interelement boundary for even-degree polynomial approximations. Optimal order error estimates measured in the energy norm are proved. Numerical examples are presented to show the performance of the method.