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Volume 9, Issue 4
A Singularly Perturbed Convection-Diffusion Problem with a Moving Interior Layer

J. L.Gracia & E. O'Riordan

Int. J. Numer. Anal. Mod., 9 (2012), pp. 823-843.

Published online: 2012-09

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  • Abstract

A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these bounds, a parameter-uniform Shishkin mesh is constructed for this problem. Numerical analysis is presented for the associated numerical method, which concludes by showing that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the theoretical bounds on the error established in the paper.

  • Keywords

Singular perturbation, interior layer, Shishkin mesh.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-823, author = {J. L.Gracia and E. O'Riordan}, title = {A Singularly Perturbed Convection-Diffusion Problem with a Moving Interior Layer}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {823--843}, abstract = {

A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these bounds, a parameter-uniform Shishkin mesh is constructed for this problem. Numerical analysis is presented for the associated numerical method, which concludes by showing that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the theoretical bounds on the error established in the paper.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/661.html} }
TY - JOUR T1 - A Singularly Perturbed Convection-Diffusion Problem with a Moving Interior Layer AU - J. L.Gracia & E. O'Riordan JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 823 EP - 843 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/661.html KW - Singular perturbation, interior layer, Shishkin mesh. AB -

A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these bounds, a parameter-uniform Shishkin mesh is constructed for this problem. Numerical analysis is presented for the associated numerical method, which concludes by showing that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the theoretical bounds on the error established in the paper.

J. L.Gracia and E. O'Riordan. (2012). A Singularly Perturbed Convection-Diffusion Problem with a Moving Interior Layer. International Journal of Numerical Analysis and Modeling. 9 (4). 823-843. doi:
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