Maximal regularity of fully discrete finite element solutions of parabolic equations

Buyang Li; Weiwei Sun

doi:10.1137/16M1071912

Maximal regularity of fully discrete finite element solutions of parabolic equations

Buyang Li, Weiwei Sun

Research output: Journal article publication › Journal article › Academic research › peer-review

17 Citations (Scopus)

Abstract

We establish the maximal lp-regularity for fully discrete finite element solutions of parabolic equations with time-dependent Lipschitz continuous coefficients. The analysis is based on a discrete lp(W1,q) estimate together with a duality argument and a perturbation method. Optimalorder error estimates of fully discrete finite element solutions in the norm of lp(Lq) follows immediately.

Original language	English
Pages (from-to)	521-542
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	55
Issue number	2
DOIs	https://doi.org/10.1137/16M1071912
Publication status	Published - 1 Jan 2017

Keywords

BDF methods
Discrete maximal parabolic regularity
Energy technique
Maximum-norm error analysis
Nonlinear parabolic equations
Time-dependent norms

ASJC Scopus subject areas

Numerical Analysis

More information

10.1137/16M1071912

http://hdl.handle.net/10397/98654

Cite this

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AB - We establish the maximal lp-regularity for fully discrete finite element solutions of parabolic equations with time-dependent Lipschitz continuous coefficients. The analysis is based on a discrete lp(W1,q) estimate together with a duality argument and a perturbation method. Optimalorder error estimates of fully discrete finite element solutions in the norm of lp(Lq) follows immediately.

KW - BDF methods

KW - Discrete maximal parabolic regularity

KW - Energy technique

KW - Maximum-norm error analysis

KW - Nonlinear parabolic equations

KW - Time-dependent norms

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U2 - 10.1137/16M1071912

DO - 10.1137/16M1071912

M3 - Journal article

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EP - 542

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 2

ER -

Maximal regularity of fully discrete finite element solutions of parabolic equations

Abstract

Keywords

ASJC Scopus subject areas

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