| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems |
| Autor/-in: | Amrein, Mario |
| et. al: | No |
| DOI: | 10.1002/mma.7351 10.48550/arXiv.2009.02505 |
| Erschienen in: | Mathematical Methods in the Applied Sciences |
| Erscheinungsdatum: | 23-Mär-2021 |
| Verlag / Hrsg. Institution: | Wiley |
| ISSN: | 0170-4214 1099-1476 |
| Sprache: | Englisch |
| Schlagwörter: | Galerkin method; High-order method |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | In this note we consider the continuous Galerkin time-stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well-known existing result for the discrete solution by applying a general linearizing procedure to the nonlinear discrete scheme including also the simplified Newton solution procedure. In particular, the presented existence results are implied by choosing sufficient small time steps locally. Furthermore, the established existence results are independent of the local approximation order. Moreover, we will see that the proposed solution scheme is able to significantly reduce the number of iterations. Finally, based on existing and well-known a priori error estimates for the discrete solution, we present some numerical experiments that highlight the proposed results of this note. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/22635 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | Lizenz gemäss Verlagsvertrag |
| Departement: | School of Management and Law |
| Organisationseinheit: | Institut für Risk & Insurance (IRI) |
| Enthalten in den Sammlungen: | Publikationen School of Management and Law |
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Zur Langanzeige
Amrein, M. (2021). Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.7351
Amrein, M. (2021) ‘Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems’, Mathematical Methods in the Applied Sciences [Preprint]. Available at: https://doi.org/10.1002/mma.7351.
M. Amrein, “Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems,” Mathematical Methods in the Applied Sciences, Mar. 2021, doi: 10.1002/mma.7351.
AMREIN, Mario, 2021. Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems. Mathematical Methods in the Applied Sciences. 23 März 2021. DOI 10.1002/mma.7351
Amrein, Mario. 2021. “Linearized Continuous Galerkin Hp-FEM Applied to Nonlinear Initial Value Problems.” Mathematical Methods in the Applied Sciences, March. https://doi.org/10.1002/mma.7351.
Amrein, Mario. “Linearized Continuous Galerkin Hp-FEM Applied to Nonlinear Initial Value Problems.” Mathematical Methods in the Applied Sciences, Mar. 2021, https://doi.org/10.1002/mma.7351.
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