Anisotropic Analysis For Q₃ Q₄ Hermite Element Of C¹ Continuity

Q₃ Hermite rectangular element of C¹ continuity is a well-known conforming element for the fourth order problem. On the regular assumption, its interpolation error estimate has been presented. In this paper, we focus on the construction of a Q₄ finite element of C¹ continuity. By using the Newton's formula of Hermite interpolation and by virtue of the property of difference quotient which we derived, the anisotropic interpolation error estimates of these two elements are obtained. This method is different from the normal one. We also give the optimal energy norms of these two elements in the fourth order problem.