Explicit Error Estimation for Boundary Value Problems

This chapter presents recent advancements in quantitative error estimates, specifically providing concrete error bounds for boundary value problems in partial differential equations. These error estimates are crucial for obtaining explicit eigenvalue bounds. A primary focus is on the a priori error estimation based on the hypercircle method (i.e., the Prager–Synge theorem), offering a novel approach for projection error estimation in the analysis of eigenvalue problems.