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...

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Detalles Bibliográficos
Autores: Shiromani, Ram, Shanthi, Vembu, Ramos Calle, Higinio
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
Descripción
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.