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

Axelsson, Owe and Karátson, János (2013) Harmonic averages, exact difference schemes and local Green's functions in variable coefficient PDE problems. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 11 (8). pp. 1441-1457. ISSN 1895-1074

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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 a Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.

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