Article
MSC:
34B05,
34E15,
35J25,
65L10,
65L60,
65L99,
65N30,
65N99,
76M10,
76R50 | MR 1125636 | Zbl 0748.65061 | DOI: 10.21136/AM.1991.104471
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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 problem with dominated convection; Petrov-Galerkin method; reaction-diffusion equation; test functions; Petrov-Galerkin method; Dirichlet problem; algorithm; numerical examples
Summary:
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.
References:
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