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

Walter Allegretto, Yanping Lin, Aihui Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-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 languageEnglish
Pages (from-to)333-354
Number of pages22
JournalNumerical Methods for Partial Differential Equations
Volume15
Issue number3
DOIs
Publication statusPublished - 1 Jan 1999
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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