Approximation Theory for the P-Version of the Finite Element Method. II

摘要

In Part II of this paper, the approximation theory developed in Part I is used to determine the piecewise polynomial approximability of solutions of elliptic problems on polygonal domains in R2 and polyhedra in R3. From these estimates, convergence orders for the p-version of the finite element method applied to such problems are readily obtained. The critical issue is the approximation of the singularities which occur at the non-smooth parts of the domain boundaries. Numerical results for two problems from two-dimensional linear elasticity are also presented. The computations show that the predicted order of convergence is achieved even for low values of p. Moreover, in contrast to the usual h-version of the finite element method, the point at which the p-version enters the asymptotic range does not depend on problem parameters such as the Poisson ratio.