A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques
نویسندگان
چکیده
We derive a posteriori error estimates for two classes of explicit finite difference schemes for ordinary differential equations. To facilitate the analysis, we derive a systematic reformulation of the finite difference schemes as finite element methods. The a posteriori error estimates quantify various sources of discretization errors, including effects arising from explicit discretization. This provides a way to judge the relative sizes of the contributions and so efficiently reduce the computational error by adjusting appropriate discretization parameters. We demonstrate the accuracy of the estimate and the behavior of various error contributions in a set of numerical examples.
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