| ¡@¡@Some fundamental issues of the approximation theory of the p-version of the finite element method will be addressed in the framework of the Jacobi-weighted Besov spaces. In this framework, the lower and upper bounds of the approximation error for singular functions are precisely analyzed, which lead to the optimal convergence of the p-version of the finite element solution for elliptic problems on non-smooth domains. Inverse approximation theorems for the p-version are also given in the same framework, which further indicates that the Jacobi-weighted Besov spaces are the proper function spaces for the analysis of the approximation of the p-version. |