Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution. (Q1410830)
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scientific article; zbMATH DE number 1993196
| Language | Label | Description | Also known as |
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| English | Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution. |
scientific article; zbMATH DE number 1993196 |
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Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution. (English)
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15 October 2003
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This paper deals with the numerical approximation of the singularly perturbed two-point boundary value problem \(-\varepsilon u''(x)- p(x) u'(x)= 0\), \(x\in (0,1)\), \(u(0)= 0\), \(u(1)= 1\), \(0<\varepsilon\ll 1\). The domain \([0,1]\) is divided into three regions: a boundary layer region, a transition region and a regular solution region. A discrete Green's function is used to obtain the uniform order of convergence, namely \(O(N^{-1}\ln N)\), where \(N\) (sufficiently large) is the total number of grid points.
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singular perturbation
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adaptive mesh
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equidistribution principle
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uniform convergence
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boundary layer
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Green's function
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two-point boundary value problem
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