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...

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Detalles Bibliográficos
Autores: Chandru, M., Das, P., Ramos Calle, Higinio
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
Descripción
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.