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arXiv · 2105.06862

Unified Analysis for Variational Time Discretizations of Higher Order and Higher Regularity Applied to Non-stiff ODEs

Simon Becher·Gunar Matthies
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Abstract

We present a unified analysis for a family of variational time discretization methods, including discontinuous Galerkin methods and continuous Galerkin-Petrov methods, applied to non-stiff initial value problems. Besides the well-definedness of the methods, the global error and superconvergence properties are analyzed under rather weak abstract assumptions which also allow considerations of a wide variety of quadrature formulas. Numerical experiments illustrate and support the theoretical results.

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Simon Becher, Gunar Matthies. 2021-05-14. Unified Analysis for Variational Time Discretizations of Higher Order and Higher Regularity Applied to Non-stiff ODEs. https://doi.org/10.1007/s11075-021-01164-z

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