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

Irene Kyza; Stephen Metcalfe

doi:10.1137/19M1264758

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

Irene Kyza
, Stephen Metcalfe

SCI Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

126 Downloads (Pure)

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.

Original language	English
Pages (from-to)	2609-2631
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	58
Issue number	5
Early online date	21 Sept 2020
DOIs	https://doi.org/10.1137/19M1264758
Publication status	Published - 2020

Keywords

Blow-up singularities
Conditional a posteriori error estimates
IMEX method
Semilinear heat equation

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/19M1264758

Author Accepted ManuscriptAccepted author manuscript, 1.59 MB

Cite this

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title = "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.",

keywords = "Blow-up singularities, Conditional a posteriori error estimates, IMEX method, Semilinear heat equation",

author = "Irene Kyza and Stephen Metcalfe",

note = "The authors acknowledge the support from the Carnegie Trust Research Incentive Grant RIG008215. S. Metcalfe acknowledges the support of the Swiss National Science Foundation (SNF) grant no. 200021-162990.",

year = "2020",

doi = "10.1137/19M1264758",

language = "English",

volume = "58",

pages = "2609--2631",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - Pointwise a posteriori error bounds for blow-up in the semilinear heat equation

AU - Kyza, Irene

AU - Metcalfe, Stephen

N1 - The authors acknowledge the support from the Carnegie Trust Research Incentive Grant RIG008215. S. Metcalfe acknowledges the support of the Swiss National Science Foundation (SNF) grant no. 200021-162990.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Blow-up singularities

KW - Conditional a posteriori error estimates

KW - IMEX method

KW - Semilinear heat equation

UR - https://www.scopus.com/pages/publications/85093074093

U2 - 10.1137/19M1264758

DO - 10.1137/19M1264758

M3 - Article

SN - 0036-1429

VL - 58

SP - 2609

EP - 2631

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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