Maximum Norm Estimate, Extrapolation and Optimal Points of Stresses for the Finite Element Methods on the Strongly Regular Triangulation

Abstract

Under the condition that the triangulation of the given domain is strongly regular, the maximum norm estimate with accuracy $O(h^2)$ of the linear finite element approximation is obtained, the optimal points of stresses at the midpoints of common sides for all adjacent elements are shown, and the estimate with higher accuracy for the extrapolation approximation based on mesh refinement and extrapolation is given.