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Volume 7, Issue 3
A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters

T. Linss

Int. J. Numer. Anal. Mod., 7 (2010), pp. 491-506.

Published online: 2010-07

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  • Abstract

A singularly perturbed two-point boundary-value problem of reaction-convection-diffusion type is considered. The problem involves two small parameters that give rise to two boundary layers of different widths. The problem is solved using a streamline-diffusion FEM (SDFEM).
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretisation error.
Numerical examples are given that illustrate the theoretical findings and verify the efficiency of the error estimator on a priori adapted meshes and in an adaptive mesh movement algorithm.

  • Keywords

Reaction-convection-diffusion problems, finite element methods, a posteriori error estimation, singular perturbation.

  • AMS Subject Headings

65L10, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-491, author = {T. Linss}, title = {A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {491--506}, abstract = {

A singularly perturbed two-point boundary-value problem of reaction-convection-diffusion type is considered. The problem involves two small parameters that give rise to two boundary layers of different widths. The problem is solved using a streamline-diffusion FEM (SDFEM).
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretisation error.
Numerical examples are given that illustrate the theoretical findings and verify the efficiency of the error estimator on a priori adapted meshes and in an adaptive mesh movement algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/733.html} }
TY - JOUR T1 - A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters AU - T. Linss JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 491 EP - 506 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/733.html KW - Reaction-convection-diffusion problems, finite element methods, a posteriori error estimation, singular perturbation. AB -

A singularly perturbed two-point boundary-value problem of reaction-convection-diffusion type is considered. The problem involves two small parameters that give rise to two boundary layers of different widths. The problem is solved using a streamline-diffusion FEM (SDFEM).
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretisation error.
Numerical examples are given that illustrate the theoretical findings and verify the efficiency of the error estimator on a priori adapted meshes and in an adaptive mesh movement algorithm.

T. Linss. (2010). A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters. International Journal of Numerical Analysis and Modeling. 7 (3). 491-506. doi:
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