An optimal C-0 finite element algorithm for the 2D biharmonic problem: theoretical analysis and numerical results

The aim of this paper is to give a new method for the numerical approximati on of the biharmonic problem. This method is based on the mixed method give n by Ciarlet-Raviart and have the same numerical properties of the Glowinsk i-Pironneau method. The error estimate associated to these methods are of o rder O(h(k-1)) for k greater than or equal to 2. The algorithm proposed in this paper converges even for k greater than or equal to 1, without any reg ularity condition on omega or,. We have an error estimate of order O(h(k)) in case of regularity.