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

Summary.

The aim of this paper is to give a new method for the numerical approximation of the biharmonic problem. This method is based on the mixed method given by Ciarlet-Raviart and have the same numerical properties of the Glowinski-Pironneau method. The error estimate associated to these methods are of order O(h$^{k-1}$) for k$\geq 2.$ The algorithm proposed in this paper converges even for k$\geq 1$, without any regularity condition on $\omega$ or $\psi$. We have an error estimate of order O(h$^k$) in case of regularity.