Robust numerical scheme for singularly perturbed convection–diffusion parabolic initial–boundary-value problems on equidistributed grids
In this article, we study the numerical solution of singularly perturbed parabolic convection–diffusion problems exhibiting regular boundary layers. To solve these problems, we use the classical upwind finite difference scheme on layer-adapted nonuniform meshes. The nonuniform meshes are obtained by...
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| Veröffentlicht in: | Computer physics communications 2014-07, Vol.185 (7), p.2008-2019 |
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| container_end_page | 2019 |
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| container_start_page | 2008 |
| container_title | Computer physics communications |
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| creator | Gowrisankar, S. Natesan, Srinivasan |
| description | In this article, we study the numerical solution of singularly perturbed parabolic convection–diffusion problems exhibiting regular boundary layers. To solve these problems, we use the classical upwind finite difference scheme on layer-adapted nonuniform meshes. The nonuniform meshes are obtained by equidistributing a positive monitor function, which depends on the second-order spatial derivative of the singular component of the solution. The truncation error and the stability analysis are obtained. Parameter-uniform error estimates are derived for the numerical solution. Semilinear IBVPs are also solved. Numerical experiments are carried out to support the theoretical results. |
| doi_str_mv | 10.1016/j.cpc.2014.04.004 |
| format | Article |
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| ispartof | Computer physics communications, 2014-07, Vol.185 (7), p.2008-2019 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Adaptive grid Boundary layers Computer simulation Derivatives Equidistribution grid Finite difference method Mathematical analysis Mathematical models Monitors Nonuniform Singularly perturbed parabolic problem Truncation errors Uniform convergence Upwind finite difference scheme |
| title | Robust numerical scheme for singularly perturbed convection–diffusion parabolic initial–boundary-value problems on equidistributed grids |
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