A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations

Abstract

The author analyzes a finite element method for the integration of initial value problems in ordinary differential equations. General and contractive problems are treated, and quasi-optimal a priori and a posteriori error bounds obtained in each case. In particular, good results are obtained for a class of stiff dissipative problems. These results are used to construct a rigorous and robust theory of global error control. The author also derives an asymptotic error estimate that is used in a discussion of the behavior of the error. In conclusion, the properties of the error control are exhibited in a series of numerical experiments.