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

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 h...

Full description

Saved in:
Bibliographic Details
Published in:Journal of scientific computing 2018-04, Vol.75 (1), p.111-127
Main Authors: Kyza, Irene, Metcalfe, Stephen, Wihler, Thomas P.
Format: Article
Language:English
Subjects:
Adaptive algorithms
Algorithms
Approximation
Boundary value problems
Computational Mathematics and Numerical Analysis
Galerkin method
Hilbert space
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Ordinary differential equations
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0565-x