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A conforming discontinuous Galerkin finite element method is introduced forsolving the biharmonic equation. This method, by its name, uses discontinuousapproximations and keeps simple formulation of the conforming finite elementmethod at the same time. The ultra simple formulation of the method will reduceprogramming complexity in practice. Optimal order error estimates in a discrete$H^2$ norm is established for the corresponding finite element solutions. Errorestimates in the $L^2$ norm are also derived with a sub-optimal order ofconvergence for the lowest order element and an optimal order of convergencefor all high order of elements. Numerical results are presented to confirm thetheory of convergence.

A conforming DG method for the biharmonic equation on polytopal meshes