A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layers.
[EN]In this article, we investigate a two-dimensional (2-D) singularly perturbed convection–reaction–diffusion elliptic type problem where two different parameters multiply the diffusion and convection terms, respectively. Furthermore, we assume that jump discontinuities exist in the source term alo...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156340 |
| Acceso en línea: | http://hdl.handle.net/10366/156340 |
| Access Level: | acceso abierto |
| Palabra clave: | Discontinuous source term Finite-difference method Shishkin mesh Elliptic equation Two singular perturbation parameters Two dimensional space 12 Matemáticas |
| Sumario: | [EN]In this article, we investigate a two-dimensional (2-D) singularly perturbed convection–reaction–diffusion elliptic type problem where two different parameters multiply the diffusion and convection terms, respectively. Furthermore, we assume that jump discontinuities exist in the source term along the x- and x-axis. Due to the presence of perturbation parameters, the solutions to such problems show boundary and corner layers. Moreover, the discontinuity in the source term adds the interior layers to the solution whose suitable numerical approach is the important goal of this article. A numerical approach is carried out using an upwind finite-difference technique that includes an appropriate layer-adapted piecewise uniform Shishkin mesh. Some examples are presented which show the good performance of the proposed method and the agreement with the theoretical analysis. |
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