Pointwise a posteriori error bounds for blow-up in the semilinear heat\n equation

2018/02/21 by Irene Kyza, Kyza, Irene, Stephen Metcalfe +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1802.07757

openalex publication_date 2018/02/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

This work is concerned with the development of a space-time adaptive\nnumerical method, based on a rigorous a posteriori error bound, for the\nsemilinear heat equation with a general local Lipschitz reaction term whose\nsolution may blow-up in finite time. More specifically, conditional a\nposteriori error bounds are derived in the L^\∞L^\∞ norm for a\nfirst order in time, implicit-explicit (IMEX), conforming finite element method\nin space discretization of the problem. Numerical experiments applied to both\nblow-up and non blow-up cases highlight the generality of our approach and\ncomplement the theoretical results.\n

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