Abstract

In this paper, a new mixed finite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains. The proposed scheme doesn’t involve any integration along mesh interfaces. The gradient of the solution is approximated by H(div)-conforming BDM k+1 element or vector valued Lagrange element with order k+1, while the solution is approximated by Lagrange element with order k+2 for any k ≥ 0. This scheme can be easily implemented and produces positive definite linear system. We provide a new discrete H2-norm stability, which is useful not only in analysis of this scheme but also in C0 interior penalty methods and DG methods. Optimal convergences in both discrete H2-norm and L2-norm are derived. This scheme with its analysis is further generalized to the von Karman equations. Finally, numerical results verifying the theoretical estimates of the proposed algorithms are also presented.