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

Owe Axelsson and János Karátson 3
  • 1 Institute of Geonics AS CR, IT4 Innovations, Studentská 1768, 708 00, Ostrava-Poruba, Czech Republic
  • 2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  • 3 Department of Applied Analysis and Computational Mathematics, ELTE University, and MTA-ELTE Numerical Analysis and Large Networks Research Group, 1117 Pázmány P. stny. 1/C, Budapest, Hungary

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.

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