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...
| Autores: | ; ; |
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| Tipo de documento: | Artigo |
| Data de publicação: | 2000 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | Inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/8502 |
| Acesso em linha: | https://hdl.handle.net/2117/8502 https://dx.doi.org/10.1016/S0045-7825(99)00193-0 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
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