Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions
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| Název: | Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions |
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| Autoři: | Ram Shiromani, Vembu Shanthi, Higinio Ramos |
| Zdroj: | GREDOS. Repositorio Institucional de la Universidad de Salamanca Universidad de Salamanca (USAL) |
| Informace o vydavateli: | Elsevier BV, 2023. |
| Rok vydání: | 2023 |
| Témata: | 12 Matemáticas, Elliptic equation, Shishkin mesh, Singular perturbation parameter, Finite difference scheme, 0101 mathematics, Two dimensional space, 01 natural sciences, Smooth convection and source terms |
| Popis: | [EN]We consider a singularly perturbed two-dimensional steady-state convection-diffusion problem with Robin boundary conditions. The coefficient of the highest-order terms in the differential equation and in the boundary conditions, denoted by ϵ, is a positive perturbation parameter, and so it may be arbitrarily small. Solutions to such problems present regular (exponential) boundary layers as well as corner layers. In this article, a numerical approach is carried out using a finite-difference technique with an appropriate layer-adapted piecewise-uniform Shishkin mesh to provide a good approximation of the exact solution. Some numerical examples are presented that show that the approximations obtained are accurate and that they are in agreement with the theoretical results. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2023.02.010 |
| Přístupová URL adresa: | http://hdl.handle.net/10366/156302 https://hdl.handle.net/10366/156302 |
| Rights: | CC BY NC ND |
| Přístupové číslo: | edsair.doi.dedup.....d723af1ef044e9a7905b1a9d3e1668c0 |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | [EN]We consider a singularly perturbed two-dimensional steady-state convection-diffusion problem with Robin boundary conditions. The coefficient of the highest-order terms in the differential equation and in the boundary conditions, denoted by ϵ, is a positive perturbation parameter, and so it may be arbitrarily small. Solutions to such problems present regular (exponential) boundary layers as well as corner layers. In this article, a numerical approach is carried out using a finite-difference technique with an appropriate layer-adapted piecewise-uniform Shishkin mesh to provide a good approximation of the exact solution. Some numerical examples are presented that show that the approximations obtained are accurate and that they are in agreement with the theoretical results. |
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| ISSN: | 01689274 |
| DOI: | 10.1016/j.apnum.2023.02.010 |