Residual-free bubbles for a singular perturbation equation

  • M. I. Asensio
  • L. P. Franca
  • A. Russo
Conference paper


We introduce a Galerkin formulation for the advective-reactive-diffusive equation. It is based on “residual-free bubble” enrichments for the test and trial spaces. An approximation of the ideal residual-free bubbles is considered and a new stabilized method is derived. The resulting formulation is proven to be stable for a wide range of coefficients and a convergence estimate is established. Numerical experiments attest to the stability and accuracy of the approach introduced.


Galerkin Method Homogeneous Dirichlet Boundary Condition Reactive Coefficient Trial Space Galerkin Formulation 
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  1. [1]
    Brezzi, F., Franca, L.P., Hughes, T.J.R., Russo, A. (1997): b = ∫ g. Comput. Methods Appl. Mech. Engrg. 145, 329–339MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Brezzi, F., Franca, L.P., Russo, A. (1998): Further considerations on residual-free bubbles for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 166, 25–33MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Brezzi, F., Russo, A. (1994): Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4, 571–587MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Brooks, A.N., Hughes, T.J.R. (1982): Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32, 199–259MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Franca, L.P., Frey, S.L., Hughes, T.J.R. (1992): Stabilized finite element methods. I. Application to the advective-diffusive model. Comput. Methods Appl. Mech. Engrg. 95, 253–276MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Franca, L.P., Russo A. (1996): Approximation of the Stokes problem by residual-free macro bubbles. East-West J. Numer. Math. 4, 265–278MathSciNetMATHGoogle Scholar
  7. [7]
    Franca, L.P., Valentin, F. (2000): On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Comput. Methods Appl. Mech. Engrg. 190, 1785–1800MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • M. I. Asensio
    • 1
  • L. P. Franca
    • 2
  • A. Russo
    • 3
    • 4
  1. 1.Departamento de Matematica AplicadaUniversidade de SalamancaSalamancaSpain
  2. 2.Department of MathematicsUniversity of ColoradoDenverUSA
  3. 3.Dipartimento di Matematica e ApplicazioniUniversità di Milano BicoccaMilanoItaly
  4. 4.IMATI-CNRPaviaItaly

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