A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
Dalík, Josef
Applications of Mathematics, Tome 36 (1991), p. 329-354 / Harvested from Czech Digital Mathematics Library
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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 $-\epsilon u^n + pu' + qu=f$ 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.

Publié le : 1991-01-01
Classification:  34B05,  34E15,  35J25,  65L10,  65L60,  65L99,  65N30,  65N99,  76M10,  76R50 
@article{104471,
     author = {Josef Dal\'\i k},
     title = {A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems},
     journal = {Applications of Mathematics},
     volume = {36},
     year = {1991},
     pages = {329-354},
     zbl = {0748.65061},
     mrnumber = {1125636},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104471}
}

Dalík, Josef. A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems. Applications of Mathematics, Tome 36 (1991) pp. 329-354. http://gdmltest.u-ga.fr/item/104471/

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