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

Abstract

This work is concerned with the development of an adaptive space-time 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∞L∞ norm for the first order (Euler) 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