$hp$-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems
Numerical Analysis
2016-12-21 v1
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.
Cite
@article{arxiv.1612.06672,
title = {$hp$-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems},
author = {Irene Kyza and Stephen Metcalfe and Thomas Wihler},
journal= {arXiv preprint arXiv:1612.06672},
year = {2016}
}