A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems

Josef Dalík

Applications of Mathematics (1991)

  • Volume: 36, Issue: 5, page 329-354
  • ISSN: 0862-7940

Abstract

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A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation - ϵ u n + p u ' + q u = f are presented and analyzed theoretically. The positive number ϵ is supposed to be much less than the discretization step and the values of p , q . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.

How to cite

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Dalík, Josef. "A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems." Applications of Mathematics 36.5 (1991): 329-354. <http://eudml.org/doc/15683>.

@article{Dalík1991,
abstract = {A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation $-\epsilon u^n + pu^\{\prime \} + qu=f$ are presented and analyzed theoretically. The positive number $\epsilon $ is supposed to be much less than the discretization step and the values of $\left|p\right|,q$. An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.},
author = {Dalík, Josef},
journal = {Applications of Mathematics},
keywords = {convection-diffusion problem with dominated convection; Petrov-Galerkin method; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples; convection-diffusion equation; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples},
language = {eng},
number = {5},
pages = {329-354},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems},
url = {http://eudml.org/doc/15683},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Dalík, Josef
TI - A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 5
SP - 329
EP - 354
AB - A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation $-\epsilon u^n + pu^{\prime } + qu=f$ are presented and analyzed theoretically. The positive number $\epsilon $ is supposed to be much less than the discretization step and the values of $\left|p\right|,q$. An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
LA - eng
KW - convection-diffusion problem with dominated convection; Petrov-Galerkin method; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples; convection-diffusion equation; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples
UR - http://eudml.org/doc/15683
ER -

References

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