Abstract
A conforming discontinuous Galerkin (CDG) C0-Pk finite element method is introduced for solving the biharmonic equation on triangular and tetrahedral meshes. A C0-Pk finite element function is a continuous and piecewise polynomial of degree k on a triangular or tetrahedral mesh. The CDG method is based on taking weak divergence on the gradient of C0-Pk finite elements. Optimal order error estimates in both a discrete H2 norm and the L2 norm are established. Numerical results are presented to verify the theory.
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