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Title: A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems (English)
Author: Dalík, Josef
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 36
Issue: 5
Year: 1991
Pages: 329-354
Summary lang: English
Category: math
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. (English)
Keyword: convection-diffusion problem with dominated convection
Keyword: Petrov-Galerkin method
Keyword: reaction-diffusion equation
Keyword: test functions
Keyword: Petrov-Galerkin method
Keyword: Dirichlet problem
Keyword: algorithm
Keyword: numerical examples
MSC: 34B05
MSC: 34E15
MSC: 35J25
MSC: 65L10
MSC: 65L60
MSC: 65L99
MSC: 65N30
MSC: 65N99
MSC: 76M10
MSC: 76R50
idZBL: Zbl 0748.65061
idMR: MR1125636
DOI: 10.21136/AM.1991.104471
Date available: 2008-05-20T18:42:10Z
Last updated: 2020-07-28
Stable URL:
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