Harmonic averages, exact difference schemes and local Green's functions in variable coefficient PDE problems

Owe Axelsson, János Karátson

Research output: Contribution to journalArticle

Abstract

A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green's functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.

Original languageEnglish
Pages (from-to)1441-1457
Number of pages17
JournalCentral European Journal of Mathematics
Volume11
Issue number8
DOIs
Publication statusPublished - Aug 1 2013

Keywords

  • Exact difference schemes
  • Harmonic averages
  • Local Green's functions
  • Singular perturbation
  • Variable coefficients

ASJC Scopus subject areas

  • Mathematics(all)

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