Geodesic
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
Applications of Mathematics, Tome 36 (1991) no. 5, pp. 329-354

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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.
DOI : 10.21136/AM.1991.104471
Classification : 34B05, 34E15, 35J25, 65L10, 65L60, 65L99, 65N30, 65N99, 76M10, 76R50
Keywords: convection-diffusion problem with dominated convection; Petrov-Galerkin method; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples 
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     author = {Dal{\'\i}k, Josef},
     title = {A {Petrov-Galerkin} approximation of convection-diffusion and reaction-diffusion problems},
     journal = {Applications of Mathematics},
     pages = {329--354},
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Dalík, Josef. A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems. Applications of Mathematics, Tome 36 (1991) no. 5, pp. 329-354. doi: 10.21136/AM.1991.104471

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