Long-time stability of finite element approximations for parabolic equations with memory

Walter Allegretto; Yanping Lin; Aihui Zhou

doi:10.1002/(SICI)1098-2426(199905)15:3&lt;333::AID-NUM5&gt;3.0.CO;2-0

Long-time stability of finite element approximations for parabolic equations with memory

Walter Allegretto, Yanping Lin, Aihui Zhou

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

10 Citations (Scopus)

Abstract

In this article, we derive the sharp long-time stability and error estimates of finite element approximations for parabolic integro-differential equations. First, the exponential decay of the solution as t → ∞ is studied, and then the semidiscrete and fully discrete approximations are considered using the Ritz-Volterra projection. Other related problems are studied as well. The main feature of our analysis is that the results are valid for both smooth and nonsmooth (weakly singular) kernels.

Original language	English
Pages (from-to)	333-354
Number of pages	22
Journal	Numerical Methods for Partial Differential Equations
Volume	15
Issue number	3
DOIs	https://doi.org/10.1002/(SICI)1098-2426(199905)15:3<333::AID-NUM5>3.0.CO;2-0
Publication status	Published - 1 Jan 1999
Externally published	Yes

Keywords

Error estimates
Finite element
Long-time
Parabolic integro-differential
Stability

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

More information

10.1002/(SICI)1098-2426(199905)15:3<333::AID-NUM5>3.0.CO;2-0

Cite this

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AU - Allegretto, Walter

AU - Lin, Yanping

AU - Zhou, Aihui

PY - 1999/1/1

Y1 - 1999/1/1

N2 - In this article, we derive the sharp long-time stability and error estimates of finite element approximations for parabolic integro-differential equations. First, the exponential decay of the solution as t → ∞ is studied, and then the semidiscrete and fully discrete approximations are considered using the Ritz-Volterra projection. Other related problems are studied as well. The main feature of our analysis is that the results are valid for both smooth and nonsmooth (weakly singular) kernels.

AB - In this article, we derive the sharp long-time stability and error estimates of finite element approximations for parabolic integro-differential equations. First, the exponential decay of the solution as t → ∞ is studied, and then the semidiscrete and fully discrete approximations are considered using the Ritz-Volterra projection. Other related problems are studied as well. The main feature of our analysis is that the results are valid for both smooth and nonsmooth (weakly singular) kernels.

KW - Error estimates

KW - Finite element

KW - Long-time

KW - Parabolic integro-differential

KW - Stability

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M3 - Journal article

SN - 0749-159X

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SP - 333

EP - 354

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -

Long-time stability of finite element approximations for parabolic equations with memory

Abstract

Keywords

ASJC Scopus subject areas

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