An error bound for approximate solutions of two-point boundary value problems (Q1825007)

This paper deals with error bounds for approximate solutions of the elliptic two-point boundary value problem \(-(py')'+qy=f,\quad y(0)=0,\quad y(1)=0.\) The error bounds presented here have two important advantages compared to those of \textit{E. C. Gartland} [SIAM J. Numer. Anal. 21, 84-100 (1984; Zbl 0561.65059)]: a) They can be applied to all kinds of approximate solutions and not only to those obtained by the Ritz method. b) The generalization to higher dimensions of the upper bound for the \(L_ 2\)-error norm poses no difficulties. Numerical experimentations with three different boundary value problems are presented.