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

Kyza, Irene and Makridakis, Charalambos (2011) Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations. SIAM Journal on Numerical Analysis, 49 (1). pp. 405-426. ISSN 0036-1429

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Abstract

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.

Item Type: Article
Schools and Departments: School of Life Sciences > Neuroscience
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Richard Chambers
Date Deposited: 21 May 2013 09:48
Last Modified: 07 Mar 2017 07:02
URI: http://sro.sussex.ac.uk/id/eprint/44785

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