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Global error control for the continuous Galerkin finite element method for ordinary differential equations. (English) Zbl 0822.65054

Authors’ abstract: We analyze a continuous Galerkin finite element method for the integration of initial value problems in ordinary differential equations. We derive quasi-optimal a priori and a posteriori error bounds. We use these results to construct a rigorous and robust theory of global error control. We conclude by exhibiting the properties of the error control in a series of numerical experiments.

MSC:

65L70 Error bounds for numerical 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
34A34 Nonlinear ordinary differential equations and systems
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References:

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