Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media

R. E. Ewing, R. D. Lazarov, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)

Abstract

Various finite volume element schemes for parabolic integro-differential equations in 1-D are derived and studied. These types of equations arise in modeling reactive flows or material with memory effects. Our main goal is to develop a general framework for obtaining finite volume element approximations and to study the error analysis. We consider the lowest-order (linear and L-splines) finite volume elements, although higher-order volume elements can be considered as well under this framework. It is proved that finite volume element approximations are convergent with optimal order in H1-norms, suboptimal order in the L2-norm and super-convergent order in a discrete H1-norm.
Original languageEnglish
Pages (from-to)157-182
Number of pages26
JournalComputing (Vienna/New York)
Volume64
Issue number2
DOIs
Publication statusPublished - 1 Jan 2000
Externally publishedYes

Keywords

  • Finite volume method
  • Integro-differential equation
  • Parabolic equation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

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