H(1)-NORM ERROR-BOUNDS FOR PIECEWISE HERMITE BICUBIC ORTHOGONAL SPLINE COLLOCATION SCHEMES FOR ELLIPTIC BOUNDARY-VALUE-PROBLEMS

Two piecewise Hermite bicubic orthogonal spline collocation schemes ar e considered for the approximate solution of elliptic nonhomogeneous D irichlet boundary value problems on rectangles. In the first scheme th e nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gauss points is used in the second scheme . The piecewise Hermite bicubic interpolant of the exact solution of t he boundary value problem is employed as a comparison function to show that the H-1-norm of the error for each scheme is O(h3).