Abstract
This 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.
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Acknowledgements
Thomas P. Wihler would like to thank the scientific committee and the local organizers of ICOSAHOM 2014 for the conference invitation to Salt Lake City. Furthermore, he acknowledges the financial support of the Swiss National Science Foundation.
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Janssen, B., Wihler, T.P. (2015). Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_7
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DOI: https://doi.org/10.1007/978-3-319-19800-2_7
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