Precise finite element error analysis by Yamamoto's explicit inversion formula for tridiagonal matrices - an extension of Babuska-Osborn's theorems

摘要

In this paper, we apply Yamamoto's explicit inversion formula for tridiagonal matrices to error analysis of the piecewise linear finite element method for two-point boundary value problems. Using the formula, we extend the theorems by Babuska-Osborn given in "Can a finite element method perform arbitrarily badly?" to a general class of two-point boundary value problems. [References: 7]