High-order accurate time-stepping schemes for convection-diffusion problems

The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function...

Descripción completa

Detalles Bibliográficos
Autores: Donea, J, Roig, B, Huerta, Antonio|||0000-0003-4198-3798
Tipo de recurso: artículo
Fecha de publicación:2000
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/8502
Acceso en línea:https://hdl.handle.net/2117/8502
https://dx.doi.org/10.1016/S0045-7825(99)00193-0
Access Level:acceso abierto
Palabra clave:Finite element method
Fluid dynamics--Mathematical models
Convection–diffusion
Time-stepping schemes
Padé approximants
Finite elements
Elements finits, Mètode dels
Dinàmica de fluids -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Àrees temàtiques de la UPC::Física::Física de fluids
Descripción
Sumario:The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function are considered for deriving multi-stage time integration schemes involving first time derivatives only, thus easier to implement in conjunction with C0 finite elements than standard time-stepping schemes which incorporate higher-order time derivatives. After a brief discussion of the stability and accuracy properties of the multi-stage Padé schemes and having underlined the similarity between Padé and Runge–Kutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.