Selections of shape functions for dimensional reduction to Helmholtz's equation

The boundary value problem of Helmholtz's equation on a n + 1 dimensional t hin slab is approximated by appropriate systems of the n-dimensional bounda ry value problem. The very detailed estimates for modeling error in the H-1 -norm demonstrate convergence when the thickness of the slab approaches 0 a s well as when the size of the systems approaches infinity. Shape functions through the thickness are first selected by finitely many eigenfunctions, and the tail is then selected to consist of polynomials. The presence of tw o types of functions gives rise to a certain choice in the selection of a p articular set of shape functions. Numerical results provide a good illustra tion of the effect of different choices for specific problems. (C) 1999 Joh n Wiley & Sons, Inc.