hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

Kyza, Irene; Metcalfe, Stephen Arthur; Wihler, Thomas (2018). hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems. Journal of scientific computing, 75(1), pp. 111-127. Springer 10.1007/s10915-017-0565-x

[img]
Preview
Text
10.1007%2Fs10915-017-0565-x.pdf - Published Version
Available under License Creative Commons: Attribution (CC-BY).

Download (657kB) | Preview

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Metcalfe, Stephen Arthur and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

0885-7474

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 08:52

Last Modified:

27 Oct 2019 22:13

Publisher DOI:

10.1007/s10915-017-0565-x

BORIS DOI:

10.7892/boris.109185

URI:

https://boris.unibe.ch/id/eprint/109185

Actions (login required)

Edit item Edit item
Provide Feedback