Unified Analysis for Variational Time Discretizations of Higher Order and Higher Regularity Applied to Non-stiff ODEs
arXiv:2105.06862 · doi:10.1007/s11075-021-01164-z
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.
35 pages