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

Irene Kyza; Stephen Metcalfe; Thomas P. Wihler

doi:10.1007/s10915-017-0565-x

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

Irene Kyza (Lead / Corresponding author)
, Stephen Metcalfe
, Thomas P. Wihler

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

235 Downloads (Pure)

Abstract

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 stucture 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.

Original language	English
Pages (from-to)	111-127
Number of pages	17
Journal	Journal of Scientific Computing
Volume	75
Early online date	27 Sept 2017
DOIs	https://doi.org/10.1007/s10915-017-0565-x
Publication status	Published - Apr 2018

Keywords

Initial value problems in Hilbert spaces
Galerkin time stepping schemes
high-order methods
blow-up singularities

Access to Document

10.1007/s10915-017-0565-xLicence: CC BY

Final Published Version
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Final published version, 653 KBLicence: CC BY

Cite this

@article{70989303254f4a77a3cf3d03ae4b4b81,

title = "hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems",

abstract = "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 stucture 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.",

keywords = "Initial value problems in Hilbert spaces, Galerkin time stepping schemes, high-order methods, blow-up singularities",

author = "Irene Kyza and Stephen Metcalfe and Wihler, \{Thomas P.\}",

note = "The authors acknowledge the support of the Swiss National Science Foundation (SNF). Funding for this research was provided by: Schweizerischer Nationalfonds zur F{\"o}rderung der Wissenschaftlichen Forschung (CH) (200021-162990) ",

year = "2018",

month = apr,

doi = "10.1007/s10915-017-0565-x",

language = "English",

volume = "75",

pages = "111--127",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer New York",

}

TY - JOUR

T1 - hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

AU - Kyza, Irene

AU - Metcalfe, Stephen

AU - Wihler, Thomas P.

N1 - The authors acknowledge the support of the Swiss National Science Foundation (SNF). Funding for this research was provided by: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (CH) (200021-162990)

PY - 2018/4

Y1 - 2018/4

N2 - 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 stucture 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.

AB - 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 stucture 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.

KW - Initial value problems in Hilbert spaces

KW - Galerkin time stepping schemes

KW - high-order methods

KW - blow-up singularities

U2 - 10.1007/s10915-017-0565-x

DO - 10.1007/s10915-017-0565-x

M3 - Article

SN - 0885-7474

VL - 75

SP - 111

EP - 127

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this