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

05/14/2021

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by   Simon Becher, et al.

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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.