# Opposing flows in a one dimensional convection-diffusion problem

Open Mathematics (2012)

- Volume: 10, Issue: 1, page 85-100
- ISSN: 2391-5455

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topEugene O’Riordan. "Opposing flows in a one dimensional convection-diffusion problem." Open Mathematics 10.1 (2012): 85-100. <http://eudml.org/doc/269267>.

@article{EugeneO2012,

abstract = {In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator to construct a parameter-uniform numerical method for this class of singularly perturbed problems.},

author = {Eugene O’Riordan},

journal = {Open Mathematics},

keywords = {Singularly perturbed; Shishkin mesh; Parameter-uniform convergence; convection-diffusion problem; singular perturbation; parameter-uniform convergence; second-order two-point boundary value problems; discontinuous coefficient; stability; error estimate; numerical example},

language = {eng},

number = {1},

pages = {85-100},

title = {Opposing flows in a one dimensional convection-diffusion problem},

url = {http://eudml.org/doc/269267},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Eugene O’Riordan

TI - Opposing flows in a one dimensional convection-diffusion problem

JO - Open Mathematics

PY - 2012

VL - 10

IS - 1

SP - 85

EP - 100

AB - In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator to construct a parameter-uniform numerical method for this class of singularly perturbed problems.

LA - eng

KW - Singularly perturbed; Shishkin mesh; Parameter-uniform convergence; convection-diffusion problem; singular perturbation; parameter-uniform convergence; second-order two-point boundary value problems; discontinuous coefficient; stability; error estimate; numerical example

UR - http://eudml.org/doc/269267

ER -

## References

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- [11] Roos H.-G., Stynes M., Tobiska L., Robust Numerical Methods for Singularly Perturbed Differential Equations, 2nd ed., Springer Ser. Comput. Math., 24, Springer, Berlin, 2008 Zbl1155.65087
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