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 |
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Pages (from-to) | 111-127 |
Number of pages | 17 |
Journal | Journal of Scientific Computing |
Volume | 75 |
Early online date | 27 Sept 2017 |
DOIs | |
Publication status | Published - Apr 2018 |
Keywords
- Initial value problems in Hilbert spaces
- Galerkin time stepping schemes
- high-order methods
- blow-up singularities