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arXiv · 1802.07757

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

Irene Kyza·Stephen Metcalfe
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Abstract

This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for the semilinear heat equation with a general local Lipschitz reaction term whose solution may blow-up in finite time. More specifically, conditional a posteriori error bounds are derived in the $L^{\infty}L^{\infty}$ norm for a first order in time, implicit-explicit (IMEX), conforming finite element method in space discretization of the problem. Numerical experiments applied to both blow-up and non blow-up cases highlight the generality of our approach and complement the theoretical results.

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Irene Kyza, Stephen Metcalfe. 2018-02-21. Pointwise a posteriori error bounds for blow-up in the semilinear heat equation. https://arxiv.org/abs/1802.07757

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