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Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

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posted on 2023-06-08, 14:59 authored by Irene Kyza, Charalambos MakridakisCharalambos Makridakis
We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank–Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

1

Volume

49

Page range

405-426

Department affiliated with

  • Neuroscience Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-05-21

First Open Access (FOA) Date

2013-05-21

First Compliant Deposit (FCD) Date

2013-05-21

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