A weak divergence CDG method for the biharmonic equation on triangular and tetrahedral meshes.

A conforming discontinuous Galerkin (CDG) C 0 - P k finite element method is introduced for solving the biharmonic equation on triangular and tetrahedral meshes. A C 0 - P k 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 C 0 - P k finite elements. Optimal order error estimates in both a discrete H 2 norm and the L 2 norm are established. Numerical results are presented to verify the theory. [ABSTRACT FROM AUTHOR]