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.

翻译：我们对一套变化时间分解方法,包括不连续的Galerkin-Petrov方法和连续的Galerkin-Petrov方法进行统一分析,这些方法适用于非固定的初始价值问题,除了方法的清晰定义外,还在相当薄弱的抽象假设下对全球错误和超级趋同特性进行了分析,这些假设还允许考虑各种各样的象形公式。 数字实验说明并支持理论结果。