Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations

Georgios Akrivis; Buyang Li; Christian Lubich

doi:10.1090/mcom/3228

Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations

Georgios Akrivis, Buyang Li, Christian Lubich

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

54 Citations (Scopus)

Abstract

We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.

Original language	English
Pages (from-to)	1527-1552
Number of pages	26
Journal	Mathematics of Computation
Volume	86
Issue number	306
DOIs	https://doi.org/10.1090/mcom/3228
Publication status	Published - 1 Jan 2017

Keywords

BDF methods
Energy technique
Maximal regularity
Maximum norm estimates
Parabolic equations
Stability

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

More information

10.1090/mcom/3228

Cite this

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AU - Li, Buyang

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N2 - We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.

AB - We analyze fully implicit and linearly implicit backward difference formula (BDF) methods for quasilinear parabolic equations, without making any assumptions on the growth or decay of the coefficient functions. We combine maximal parabolic regularity and energy estimates to derive optimal-order error bounds for the time-discrete approximation to the solution and its gradient in the maximum norm and energy norm.

KW - BDF methods

KW - Energy technique

KW - Maximal regularity

KW - Maximum norm estimates

KW - Parabolic equations

KW - Stability

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DO - 10.1090/mcom/3228

M3 - Journal article

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EP - 1552

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JF - Mathematics of Computation

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ER -

Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations

Abstract

Keywords

ASJC Scopus subject areas

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