Space-time approximation of parabolic systems with variable growth

Dominic Breit; Prince Romeo Mensah

doi:10.1093/IMANUM/DRZ039

Space-time approximation of parabolic systems with variable growth

Dominic Breit, Prince Romeo Mensah

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Abstract

We study a parabolic system with p(t,x)-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element-based space-time approximation. The error is measured in the quasi norm and the result holds if the exponent p(t,x) is (αt,αx)-Hölder continuous.

Original language	English
Pages (from-to)	2505–2552
Number of pages	48
Journal	IMA Journal of Numerical Analysis
Volume	40
Issue number	4
Early online date	18 Nov 2019
DOIs	https://doi.org/10.1093/IMANUM/DRZ039
Publication status	Published - Oct 2020

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10.1093/IMANUM/DRZ039

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This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record IMA Journal of Numerical Analysis, Volume 40, Issue 4, October 2020, Pages 2505–2552 is available online at: https://doi.org/10.1093/imanum/drz039
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title = "Space-time approximation of parabolic systems with variable growth",

abstract = "We study a parabolic system with p(t,x)-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element-based space-time approximation. The error is measured in the quasi norm and the result holds if the exponent p(t,x) is (αt,αx)-H{\"o}lder continuous.",

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N2 - We study a parabolic system with p(t,x)-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element-based space-time approximation. The error is measured in the quasi norm and the result holds if the exponent p(t,x) is (αt,αx)-Hölder continuous.

AB - We study a parabolic system with p(t,x)-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element-based space-time approximation. The error is measured in the quasi norm and the result holds if the exponent p(t,x) is (αt,αx)-Hölder continuous.

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DO - 10.1093/IMANUM/DRZ039

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Space-time approximation of parabolic systems with variable growth

Abstract

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