COLLOCATION CUBIC ELEMENTS FOR ELLIPTIC-EQUATIONS

The standard cubic Lagrange and Hermite triangular elements need ten nodal values in two dimensional problems. The collocation cubic elements, introduced in [1], use only nine nodal values and collocation at the centroid. It is still a conforming method. For some simple model problems, we can prove that the order of convergence of the collocation method is the same as the order of convergence for the corresponding standard cubic element. The proof given in [1] contained a mistake. In this paper we present a correct proof.