OPTIMAL-ORDER FINITE DIFFERENCE APPROXIMATION OF GENERALIZED SOLUTIONS TO THE BIHARMONIC EQUATION IN A CUBE.

We prove an optimal-order error bound in the discrete H2() norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in n space dimensions, with n 2 f2; : : : ; 7g, whose generalized solution belongs to the Sobolev space Hs()\H2 0 () for 1 2 max(5; n) < s 4, where = (0; 1)n. The result extends the range of the Sobolev index s in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of Hs() into C() in n space dimensions. [ABSTRACT FROM AUTHOR]