Maximum-norm stability and maximal Lp regularity of FEMs for parabolic equations with Lipschitz continuous coefficients

Buyang Li

doi:10.1007/s00211-015-0698-5

Maximum-norm stability and maximal Lp regularity of FEMs for parabolic equations with Lipschitz continuous coefficients

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

Abstract

In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximum-norm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT) and Lp((0,T); Lp(Ω)), 1 < p, q < ∞. The maximal Lp regularity of the parabolic finite element equation is also established.

Original language	English
Pages (from-to)	489-516
Number of pages	28
Journal	Numerische Mathematik
Volume	131
Issue number	3
DOIs	https://doi.org/10.1007/s00211-015-0698-5
Publication status	Published - 13 Nov 2015
Externally published	Yes

Keywords

35K20
65M12
65M30

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1007/s00211-015-0698-5

Cite this

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abstract = "In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximum-norm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT) and Lp((0,T); Lp(Ω)), 1 < p, q < ∞. The maximal Lp regularity of the parabolic finite element equation is also established.",

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AB - In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximum-norm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT) and Lp((0,T); Lp(Ω)), 1 < p, q < ∞. The maximal Lp regularity of the parabolic finite element equation is also established.

KW - 35K20

KW - 65M12

KW - 65M30

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DO - 10.1007/s00211-015-0698-5

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JO - Numerische Mathematik

JF - Numerische Mathematik

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ER -

Maximum-norm stability and maximal L<sup>p</sup> regularity of FEMs for parabolic equations with Lipschitz continuous coefficients

Abstract

Keywords

ASJC Scopus subject areas

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