A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data
type: Item
instance of: scholarly article
title: A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data
zbMATH Open document ID: 1107.65069
DOI: 10.1007/BF02896481
author: N. E. Zubov
published in: Journal of Applied Mathematics and Computing
publication date: 2006-12-04T00:00:00Z
review text: A numerical method is suggested for singularly perturbed boundary-value problems with finite jump discontinuity in the convection coefficient, and the source term at an interior point. Because of the discontinuity in the data, these problems possess an interior layer in addition to the boundary layers. Here, the authors propose a Petrov-Galerkin finite element method with piecewise-exponential test functions and piecewise-linear trial functions. The point of discontinuity of the coefficient is handled carefully. First-order \(\varepsilon\)-uniform error estimates are proved. A numerical example is carried out to verify the theoretical results.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 5076955
zbMATH Keywords: singular perturbation
zbMATH Keywords: Petrov-Galerkin finite element method
zbMATH Keywords: uniform convergence
zbMATH Keywords: interior layer
zbMATH Keywords: boundary layers
zbMATH Keywords: error estimates
zbMATH Keywords: numerical example
Wikidata QID: Q115391240
reviewed by: Srinivasan Natesan
MaRDI profile type: Publication
cites work: Q4944499
cites work: Q4485828
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cites work: A computationally efficient solution technique for moving-boundary problems in finite media
cites work: The use of a modified Petrov-Galerkin method for gas-sold reaction modelling
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full work available at URL: https://doi.org/10.1007/bf02896481
OpenAlex ID: W2084939480
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description: scientific article; zbMATH DE number 5076955