Volume 5, Issue 4
Uniform Convergence via Preconditioning.

RELJA VULANOVI ́C AND TH ́AI ANH NHAN

Int. J. Numer. Anal. Mod. B,5 (2014), pp. 347-356

Published online: 2014-05

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  • Abstract
The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.
  • AMS Subject Headings

65L10 65L12 65L20 65L70

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-5-347, author = {RELJA VULANOVI ́C AND TH ́AI ANH NHAN}, title = { Uniform Convergence via Preconditioning.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2014}, volume = {5}, number = {4}, pages = {347--356}, abstract = {The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/239.html} }
TY - JOUR T1 - Uniform Convergence via Preconditioning. AU - RELJA VULANOVI ́C AND TH ́AI ANH NHAN JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 347 EP - 356 PY - 2014 DA - 2014/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/239.html KW - singular perturbation KW - convection-diffusion KW - boundary-value problem KW - Shishkin mesh KW - finite differences KW - uniform convergence KW - preconditioning AB - The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on the Shishkin mesh is analyzed. A new, conceptually simple proof of pointwise convergence uniform in the perturbation parameter is provided. The proof is based on the preconditioning of the discrete system.
RELJA VULANOVI ́C AND TH ́AI ANH NHAN. (2014). Uniform Convergence via Preconditioning.. International Journal of Numerical Analysis Modeling Series B. 5 (4). 347-356. doi:
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