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Volume 10, Issue 2
Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points

C.-Y. Jung & T. B. Nguyen

Int. J. Numer. Anal. Mod., 10 (2013), pp. 314-332.

Published online: 2013-10

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  • Abstract

In this article we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and it shows 2nd-order convergence in the approximations.

  • Keywords

Convection-diffusion equations, Singular perturbation analysis, Transition layers, Boundary layers, Compatibility conditions, Turning points, Finite volume methods.

  • AMS Subject Headings

34E15, 80M35, 76R50, 35B40, 80M12

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-10-314, author = {Jung , C.-Y. and Nguyen , T. B.}, title = {Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {2}, pages = {314--332}, abstract = {

In this article we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and it shows 2nd-order convergence in the approximations.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/570.html} }
TY - JOUR T1 - Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points AU - Jung , C.-Y. AU - Nguyen , T. B. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 314 EP - 332 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/570.html KW - Convection-diffusion equations, Singular perturbation analysis, Transition layers, Boundary layers, Compatibility conditions, Turning points, Finite volume methods. AB -

In this article we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and it shows 2nd-order convergence in the approximations.

Jung , C.-Y. and Nguyen , T. B.. (2013). Semi-Analytical Numerical Methods for Convection-Dominated Problems with Turning Points. International Journal of Numerical Analysis and Modeling. 10 (2). 314-332. doi:
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