SUMMARYThis paper deals with solving two-dimensional variational problems of second-and third-order by the finite element method. To each meshpoint are associated three or six basic functions of class C1 or Cz. The expression of the admissible functions on a triangular and rectangular element are given here in a general form which is specially suitable for computation.

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This paper describes two finite elements of C'-class defined on a tetrahedron. In order to define these elements we give the corresponding function spaces in explicit form. w(x, Y , z):= (x, Y , 2) a2(xr y , z):= (1 -x -y -2, x, y ) W(X, y , 2):= (2, 1 -x -y -2, x) a4(x, y , z):= ( y , 2, 1 -xy -2 ) effect cyclic permutations of the numbering of the vertices of $.The space V has dimension sixteen. It will be defined by the Lagrange basis {uin: S + W, i = 1(1)4, n = 0(1)3} given in subsection 3.3. The solution of an interpolation problem (iii) is then simply 4 3 u = 2: 2: CinUin.i-1 n-0

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