Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems

Amrein, Mario

doi:10.1002/mma.7351

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems
Authors:	Amrein, Mario
et. al:	No
DOI:	10.1002/mma.7351 10.48550/arXiv.2009.02505
Published in:	Mathematical Methods in the Applied Sciences
Issue Date:	23-Mar-2021
Publisher / Ed. Institution:	Wiley
ISSN:	0170-4214 1099-1476
Language:	English
Subjects:	Galerkin method; High-order method
Subject (DDC):	510: Mathematics
Abstract:	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
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Management and Law
Organisational Unit:	Institute for Risk & Insurance (IRI)
Appears in collections:	Publikationen School of Management and Law

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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.