PREWAVELET APPROXIMATIONS FOR A SYSTEM OF BOUNDARY INTEGRAL-EQUATIONSFOR PLATES WITH FREE EDGES ON POLYGONS

We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with doubl e layer potentials whose variational formulation was given in Referenc e 25. We approximate its solution (u, (partial derivative u/partial de rivative n)) by the Galerkin method with approximated spaces made of p iecewise polynomials of order 2 and 1 for, respectively, u and (partia l derivative u/partial derivative n). A prewavelet basis of these subs paces is built and equivalences between some Sobolev norms and discret e ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N-2) to O(N log N), where N is the size of this matrix. We finally show that the compress ed stiffness matrices have a condition number uniformly bounded with r espect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. (C) 1998 B. G. Teubner Stuttgart-Joh n Wiley & Sons, Ltd.