A posteriori error bounds and global error control for approximation of ordinary differential equations. (English) Zbl 0820.65052

Using a discontinuous Galerkin finite element method for the integration of initial value problems in ordinary differential equations in conjunction with a discrete Gronwall inequality the author combines a priori and a posteriori analyses of the error to construct a rigorous theory of global error control, using information obtained from computable quantities. The a posteriori analysis he presents suggests a new approach to the theory of adaptive error control useful for stiff problems.
The discussion is concluded by exhibiting the behavior of that error control method in a variety of test problems and by demonstrating the validity of the method in giving realistic estimates of the global error and in detecting superstability in the knee problem.


65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A30 Linear ordinary differential equations and systems
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