|Publication type:||Article in scientific journal|
|Type of review:||Peer review (publication)|
|Title:||Linearized continuous Galerkin hp-FEM applied to nonlinear initial value problems|
|Published in:||Mathematical Methods in the Applied Sciences|
|Publisher / Ed. Institution:||Wiley|
|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.|
|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. “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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