A Petrov-Galerkin approximation of convection-diffusion and reaction- diffusion problems (Q1184930)
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scientific article; zbMATH DE number 35316
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Petrov-Galerkin approximation of convection-diffusion and reaction- diffusion problems |
scientific article; zbMATH DE number 35316 |
Statements
A Petrov-Galerkin approximation of convection-diffusion and reaction- diffusion problems (English)
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28 June 1992
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A new construction of test functions in the Petrov-Galerkin method is described. Using this construction, the author proposes algorithms for solving the Dirichlet problem for the differential equation \(-\varepsilon u''+pu'+qu=f\), where the positive number \(\varepsilon\) is supposed to be much less than the discretization step and the values of \(| p|\), \(q\). An algorithm for the corresponding two-dimensional problem is also suggested and numerical examples are given to demonstrate the effectiveness of the proposed algorithms.
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convection-diffusion equation
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reaction-diffusion equation
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test functions
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Petrov-Galerkin method
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Dirichlet problem
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algorithm
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numerical examples
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