A C 0 finite element method for the biharmonic problem without extrinsic penalization

A symmetric C0 finite element method for the biharmonic problem is constructed and analyzed. In our approach, we introduce one-sided discrete second-order derivatives and Hessian matrices to formulate our scheme. We show that the method is stable and converge with optimal order in a variety of norms. A distinctive feature of the method is that the results hold without extrinsic penalization of the gradient across interelement boundaries. Numerical experiments are given that support the theoretical results, and the extension to Kirchhoff plates is also discusse