A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Element

摘要

We consider a numerical method to get a guaranteed bound of the optimal constant in the error estimates of a finite element method with linear triangular elements in the plane. The problem is reduced to a king of smallest eigenvalue problem for an elliptic operator in a certain function space on the reference triangle. In order to solve the problem, we formulate a numerical verification procedure based on finite element approximations and constuctive error estimates.