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Volume 7, Issue 3
Finite Volume Approximation of Two-Dimensional Stiff Problems

C.-Y. Jung & R. Temam

Int. J. Numer. Anal. Mod., 7 (2010), pp. 462-476.

Published online: 2010-07

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  • Abstract

Continuing an earlier work in space dimension one, the aim of this article is to present, in space dimension two, a novel method to approximate stiff problems using a combination of (relatively easy) analytical methods and finite volume discretization. The stiffness is caused by a small parameter in the equation which introduces ordinary and corner boundary layers along the boundaries of a two-dimensional rectangle domain. Incorporating in the finite volume space the boundary layer correctors, which are explicitly found by analysis, the boundary layer singularities are absorbed and thus uniform meshes can be preferably used. Using the central difference scheme at the volume interfaces, the proposed scheme finally appears to be an efficient second-order accurate one.

  • Keywords

Finite volume methods, boundary layers, correctors, asymptotic analysis, singularly perturbed problems, stiff problems.

  • AMS Subject Headings

34D15, 76N20

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-7-462, author = {Jung , C.-Y. and Temam , R.}, title = {Finite Volume Approximation of Two-Dimensional Stiff Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {462--476}, abstract = {

Continuing an earlier work in space dimension one, the aim of this article is to present, in space dimension two, a novel method to approximate stiff problems using a combination of (relatively easy) analytical methods and finite volume discretization. The stiffness is caused by a small parameter in the equation which introduces ordinary and corner boundary layers along the boundaries of a two-dimensional rectangle domain. Incorporating in the finite volume space the boundary layer correctors, which are explicitly found by analysis, the boundary layer singularities are absorbed and thus uniform meshes can be preferably used. Using the central difference scheme at the volume interfaces, the proposed scheme finally appears to be an efficient second-order accurate one.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/731.html} }
TY - JOUR T1 - Finite Volume Approximation of Two-Dimensional Stiff Problems AU - Jung , C.-Y. AU - Temam , R. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 462 EP - 476 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/731.html KW - Finite volume methods, boundary layers, correctors, asymptotic analysis, singularly perturbed problems, stiff problems. AB -

Continuing an earlier work in space dimension one, the aim of this article is to present, in space dimension two, a novel method to approximate stiff problems using a combination of (relatively easy) analytical methods and finite volume discretization. The stiffness is caused by a small parameter in the equation which introduces ordinary and corner boundary layers along the boundaries of a two-dimensional rectangle domain. Incorporating in the finite volume space the boundary layer correctors, which are explicitly found by analysis, the boundary layer singularities are absorbed and thus uniform meshes can be preferably used. Using the central difference scheme at the volume interfaces, the proposed scheme finally appears to be an efficient second-order accurate one.

Jung , C.-Y. and Temam , R.. (2010). Finite Volume Approximation of Two-Dimensional Stiff Problems. International Journal of Numerical Analysis and Modeling. 7 (3). 462-476. doi:
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