Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

Abstract

AbstractThis article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in \(\mathbb{R}^{n}\), with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from Janssen and Wihler (Existence results for the continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems, 2014, Submitted), and provide a numerical comparison of the two time discretization methods.KeywordsTime-stepping GalerkinNonlinear Initial Value ProblemsDiscontinuous Galerkin Time-stepping MethodRecent Existence ResultsLipschitz Continuous NonlinearitiesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.