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Volume 7, Issue 3
An Enriched Subspace Finite Element Method for Convection-Diffusion Problems

R. B. Kellogg & C. Xenophontos

Int. J. Numer. Anal. Mod., 7 (2010), pp. 477-490.

Published online: 2010-07

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  • Abstract

We consider a one-dimensional convection-diffusion boundary value problem, whose solution contains a boundary layer at the outflow boundary, and construct a finite element method for its approximation. The finite element space consists of piecewise polynomials on a uniform mesh but is enriched by a finite number of functions that represent the boundary layer behavior. We show that this method converges at the optimal rate, independently of the singular perturbation parameter, when the error is measured in the energy norm associated with the problem. Numerical results confirming the theory are also presented, which also suggest that in the case of variable coefficients, the number of enrichment functions need not be as high as the theory suggests.

  • Keywords

Finite element method, boundary layers, enriched subspace.

  • AMS Subject Headings

65N30, 65N15, 65L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-477, author = {R. B. Kellogg and C. Xenophontos}, title = {An Enriched Subspace Finite Element Method for Convection-Diffusion Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {477--490}, abstract = {

We consider a one-dimensional convection-diffusion boundary value problem, whose solution contains a boundary layer at the outflow boundary, and construct a finite element method for its approximation. The finite element space consists of piecewise polynomials on a uniform mesh but is enriched by a finite number of functions that represent the boundary layer behavior. We show that this method converges at the optimal rate, independently of the singular perturbation parameter, when the error is measured in the energy norm associated with the problem. Numerical results confirming the theory are also presented, which also suggest that in the case of variable coefficients, the number of enrichment functions need not be as high as the theory suggests.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/732.html} }
TY - JOUR T1 - An Enriched Subspace Finite Element Method for Convection-Diffusion Problems AU - R. B. Kellogg & C. Xenophontos JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 477 EP - 490 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/732.html KW - Finite element method, boundary layers, enriched subspace. AB -

We consider a one-dimensional convection-diffusion boundary value problem, whose solution contains a boundary layer at the outflow boundary, and construct a finite element method for its approximation. The finite element space consists of piecewise polynomials on a uniform mesh but is enriched by a finite number of functions that represent the boundary layer behavior. We show that this method converges at the optimal rate, independently of the singular perturbation parameter, when the error is measured in the energy norm associated with the problem. Numerical results confirming the theory are also presented, which also suggest that in the case of variable coefficients, the number of enrichment functions need not be as high as the theory suggests.

R. B. Kellogg and C. Xenophontos. (2010). An Enriched Subspace Finite Element Method for Convection-Diffusion Problems. International Journal of Numerical Analysis and Modeling. 7 (3). 477-490. doi:
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