Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data
[EN]In the present work, we consider a parabolic convection-diffusion-reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively. In addition, we assume that the convection coefficient and the source term of the partial differential equation have a...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/154400 |
| Acceso en línea: | http://hdl.handle.net/10366/154400 |
| Access Level: | acceso abierto |
| Palabra clave: | Initial-boundary value problem Interior and boundary layer phenomena Non-smooth data Parabolic convection-diffusion problem Parameter uniformly convergent method Shishkin-type mesh Singular perturbation Two-parameter singularly perturbed problem 1299 Otras Especialidades Matemáticas |
| Sumario: | [EN]In the present work, we consider a parabolic convection-diffusion-reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively. In addition, we assume that the convection coefficient and the source term of the partial differential equation have a jump discontinuity. The presence of perturbation parameters leads to the boundary and interior layers phenomenawhose appropriate numerical approximation is themain goal of this paper. We have developed a uniform numerical method, which converges almost linearly in space and time on a piecewise uniform space adaptive Shishkin-type mesh and uniform mesh in time. Error tables based on several examples show the convergence of the numerical solutions. In addition, several numerical simulations are presented to show the effectiveness of resolving layer behavior and their locations. |
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