SUPG-based stabilization using a separated representations approach

We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG sc...

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Detalles Bibliográficos
Autores: González, D., Debeugny, L., Cueto, E., Chinesta, F., Díez, Pedro|||0000-0001-6464-6407, Huerta, Antonio|||0000-0003-4198-3798
Tipo de recurso: artículo
Fecha de publicación:2010
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:2117/10251
Acceso en línea:https://hdl.handle.net/2117/10251
https://dx.doi.org/10.1007/s12289-010-0909-7
Access Level:acceso abierto
Palabra clave:Numerical methods and algorithms
Finite element method
Differential equations, Partial
Anàlisi numèrica
Elements finits, Mètode dels
Equacions diferencials parcials
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Descripción
Sumario:We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known.