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

Open Mathematics (2013)

- Volume: 11, Issue: 8, page 1441-1457
- ISSN: 2391-5455

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topOwe Axelsson, and János Karátson. "Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems." Open Mathematics 11.8 (2013): 1441-1457. <http://eudml.org/doc/269454>.

@article{OweAxelsson2013,

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.},

author = {Owe Axelsson, János Karátson},

journal = {Open Mathematics},

keywords = {Variable coefficients; Harmonic averages; Singular perturbation; Local Green’s functions; Exact difference schemes; variable coefficients; harmonic averages; singular perturbation; local Green's functions; exact difference schemes; convection-reaction equation; error estimates; Darcy flow; method of characteristics; transport equations; Petrov-Galerkin finite element method},

language = {eng},

number = {8},

pages = {1441-1457},

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

url = {http://eudml.org/doc/269454},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Owe Axelsson

AU - János Karátson

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

JO - Open Mathematics

PY - 2013

VL - 11

IS - 8

SP - 1441

EP - 1457

AB - 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.

LA - eng

KW - Variable coefficients; Harmonic averages; Singular perturbation; Local Green’s functions; Exact difference schemes; variable coefficients; harmonic averages; singular perturbation; local Green's functions; exact difference schemes; convection-reaction equation; error estimates; Darcy flow; method of characteristics; transport equations; Petrov-Galerkin finite element method

UR - http://eudml.org/doc/269454

ER -

## References

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