Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions.
[EN]In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/156978 |
| Acceso en línea: | http://hdl.handle.net/10366/156978 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary layers Robin boundary conditions Adaptive mesh Equidistribution principle |
| Sumario: | [EN]In this work we develop a parameter-uniform numerical method on equidistributed meshes for solving a class of singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions. The discretization consists of a modified Euler scheme in time, a central difference scheme in space, and a special finite difference scheme for the Robin boundary conditions. A uniform mesh is used in the time direction while the mesh in the space direction is generated via the equidistribution of a suitably chosen monitor function. We discuss error analysis and prove that the method is parameter-uniformly convergent of order two in space and order one in time. To support the theoretical result, some numerical experiments are performed. |
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