SUPG-based stabilization using a separated representations approach

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.contributor.author	González, D.
dc.contributor.author	Debeugny, L.
dc.contributor.author	Cueto, E.
dc.contributor.author	Chinesta, F.
dc.contributor.author	Díez, Pedro
dc.contributor.author	Huerta, Antonio
dc.date	2010-04
dc.identifier.citation	González, D. [et al.]. SUPG-based stabilization using a separated representations approach. "International journal of material forming", Abril 2010, vol. 3, núm. 1, p. 883-886.
dc.identifier.citation	1960-6206
dc.identifier.citation	10.1007/s12289-010-0909-7
dc.identifier.uri	http://hdl.handle.net/2117/10251
dc.language.iso	eng
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
dc.subject	Numerical methods and algorithms
dc.subject	Finite element method
dc.subject	Differential equations, Partial
dc.subject	Anàlisi numèrica
dc.subject	Elements finits, Mètode dels
dc.subject	Equacions diferencials parcials
dc.title	SUPG-based stabilization using a separated representations approach
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	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.

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