Semi-discrete finite element approximations for linear parabolic integro-differential equations with integrable kernels

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Abstract

In this paper we consider finite element methods for general parabolic integro-differential equations with integrable kernels. A new approach is taken, which allows us to derive optimal Lp, 2 ≤ p ≤ ∞, error estimates and superconvergence. The main advantage of our method is that the semi-discrete finite element approximations for linear equations, with both smooth and integrable kernels, can be treated in the same way without the introduction of the Ritz-Volterra projection; therefore, one can make full use of the results of finite element approximations for elliptic problems.
Original languageEnglish
Pages (from-to)51-83
Number of pages33
JournalJournal of Integral Equations and Applications
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Dec 1998
Externally publishedYes

Keywords

  • Error estimates
  • Finite element
  • Integrable kernel
  • Integro-differential
  • Maximum norm
  • Parabolic
  • Superconvergence

ASJC Scopus subject areas

  • Numerical Analysis
  • Applied Mathematics

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