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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Bibliographic Details
Published in:International journal of material forming Vol. 3; no. Suppl 1; pp. 883 - 886
Main Authors: González, D., Debeugny, L., Cueto, E., Chinesta, F., Díez, P., Huerta, A.
Format: Journal Article Publication
Language:English
Published: Paris Springer-Verlag 01.04.2010
Springer Verlag
Subjects:
Anàlisi numèrica
CAE) and Design
Computational Intelligence
Computer-Aided Engineering (CAD
Differential equations, Partial
Elements finits, Mètode dels
Engineering
Engineering Sciences
Equacions diferencials parcials
Finite element method
Machines
Manufacturing
Matemàtiques i estadística
Materials Science
Mechanical Engineering
Mechanics
Mètodes numèrics
New and advanced numerical strategies for material forming: E. Cueto
Numerical methods and algorithms
Processes
Àrees temàtiques de la UPC
Proper Generalized Decomposition
Finite Sum Decomposition
Separated Representations
SUPG
Convection-diffusion equation
ISSN:1960-6206, 1960-6214
Online Access:Get full text
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Summary: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.
ISSN:1960-6206
1960-6214
DOI:10.1007/s12289-010-0909-7