THE h-p VERSION OF THE FINITE ELEMENT METHOD FOR DOMAINS WITH CURVED BOUNDARIES*

Abstract. This paper analyzes the convergence of the h-p version of the finite element method for elliptic problems on curved domains. It proves that when the boundary of the domain is piecewise analytic, boundary conditions are piecewise analytic, and the sides of the elements are analytic, the h-p version has an exponential rate of convergence. Numerical computations are included. The paper generalizes the results previously obtained by the authors The h-p version offinite element method, Part 1: The basic approximation results, Comp. Mech., (1986), pp. 21-41], The h-p version offinite element method, Part 2: General results and applications, Comp. Mech., (1986), pp. 203-220]. Key words, finite element method, h-p version, curved boundary with corners, nonhomogeneous essential boundary conditions AMS(MOS) subject classifications. 35A40, 65N30 1. Introduction. Th