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

Applications of Mathematics (1991)

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

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topDalík, 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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