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Volume 7, Issue 4
A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems

T. Linss & N. Kopteva

Int. J. Numer. Anal. Mod., 7 (2010), pp. 718-733.

Published online: 2010-07

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  • Abstract

We consider a two-point boundary-value problem for a singularly perturbed convection-diffusion problem. The problem is solved by using a defect-correction method based on a first-order upwind difference scheme and a second-order (unstabilized) central difference scheme.
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretization 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

Convection-diffusion problems, finite difference schemes, defect correction, a posteriori error estimation, singular perturbation.

  • AMS Subject Headings

65L10, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-7-718, author = {T. Linss and N. Kopteva}, title = {A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {4}, pages = {718--733}, abstract = {

We consider a two-point boundary-value problem for a singularly perturbed convection-diffusion problem. The problem is solved by using a defect-correction method based on a first-order upwind difference scheme and a second-order (unstabilized) central difference scheme.
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretization 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/748.html} }
TY - JOUR T1 - A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems AU - T. Linss & N. Kopteva JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 718 EP - 733 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/748.html KW - Convection-diffusion problems, finite difference schemes, defect correction, a posteriori error estimation, singular perturbation. AB -

We consider a two-point boundary-value problem for a singularly perturbed convection-diffusion problem. The problem is solved by using a defect-correction method based on a first-order upwind difference scheme and a second-order (unstabilized) central difference scheme.
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretization 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 and N. Kopteva. (2010). A Posteriori Error Estimation for a Defect-Correction Method Applied to Convection-Diffusion Problems. International Journal of Numerical Analysis and Modeling. 7 (4). 718-733. doi:
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