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SUPG-based stabilization using a separated representations approach

  • New and advanced numerical strategies for material forming: E. Cueto
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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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References

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Authors and Affiliations

  1. Group of Structural Mechanics and Material Modelling, Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza, Zaragoza, Spain

    D. González, L. Debeugny & E. Cueto

  2. GeM UMR CNRS-ECN, École Centrale de Nantes, Nantes, France

    F. Chinesta

  3. Laboratori de Càlcul Numèric, Universitat Politècnica de Catalunya, Barcelona, Spain

    P. Díez & A. Huerta

Authors
  1. D. González
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  2. L. Debeugny
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  3. E. Cueto
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  4. F. Chinesta
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  5. P. Díez
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  6. A. Huerta
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Corresponding author

Correspondence to D. González.

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González, D., Debeugny, L., Cueto, E. et al. SUPG-based stabilization using a separated representations approach. Int J Mater Form 3 (Suppl 1), 883–886 (2010). https://doi.org/10.1007/s12289-010-0909-7

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  • DOI: https://doi.org/10.1007/s12289-010-0909-7

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