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Residual-free bubbles for a singular perturbation equation

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. I. Asensio

    (Universidade de Salamanca, Departamento de Matematica Aplicada)

  • L. P. Franca

    (University of Colorado, Department of Mathematics)

  • A. Russo

    (Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni
    IMATI-CNR)

Abstract

Summary 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.

Suggested Citation

  • M. I. Asensio & L. P. Franca & A. Russo, 2003. "Residual-free bubbles for a singular perturbation equation," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 21-34, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_2
    DOI: 10.1007/978-88-470-2089-4_2
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