Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions

摘要

This paper will analyze the lower and upper error bounds of the finite element solution of the p-version for linear elliptic problems in polygonal domains. The optimal rate of convergence is rigorously proved based on the sharp estimates of lower and upper bounds of the approximation error. Mathematics Subject Classification (1991): 65N30. [References: 13]