SUPG-based stabilization using a separated representations approach

Author (s): González, D.; Debeugny, L.; Cueto, E.; Chinesta, F.; Díez, P. and Huerta, A.
Journal: International Journal of Material Forming

Volume: 3
Pages: 883 – 886
Date: 2010

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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Bibtex:

@article{2010-IJMF-GDCCDH,
  Author   = {Gonz{\'a}lez, D.; Debeugny, L.; Cueto, E.; Chinesta, F.; D{\'\i}ez, P. and Huerta, A.},
  Title    = {SUPG-based stabilization using a separated representations approach},
  Fjournal = {International Journal of Material Forming},
  Journal  = {Int. J. Mater. Form.},
  Volume   = {3},
  Number   = {1},
  Pages    = {883--886},
  Year     = {2010}}