Residual-free bubbles for a singular perturbation equation

  1. Asensio, M. I. 4
  2. Franca, L. P. 3
  3. Russo, A. 12
  1. 1 Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Milano, Italy
  2. 2 IMATI-CNR, Pavia, Italy
  3. 3 Department of Mathematics, University of Colorado, Denver, CO, USA
  4. 4 Departamento de Matemática Aplicada, Universidad de Salamanca, Salamanca, Spain
Mostrar afiliaciones +
Libro:
Numerical Mathematics and Advanced Applications : Proceedings of ENUMATH 2001 the 4th European Conference on Numerical Mathematics and Advanced Applications Ischia, July 2001

ISBN: 9788847021679,  9788847020894,  9788847001800

Año de publicación: 2003

Páginas: 21-34

Tipo: Capítulo de Libro

DOI: 10.1007/978-88-470-2089-4_2 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

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.

Referencias bibliográficas

  • Brezzi, F., Franca, L.P., Hughes, T.J.R., Russo, A. (1997): b = ∫ g. Comput. Methods Appl. Mech. Engrg. 145, 329–339
  • Brezzi, F., Franca, L.P., Russo, A. (1998): Further considerations on residual-free bubbles for advective-diffusive equations. Comput. Methods Appl. Mech. Engrg. 166, 25–33
  • Brezzi, F., Russo, A. (1994): Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci. 4, 571–587
  • 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, 199–259
  • 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, 253–276
  • Franca, L.P., Russo A. (1996): Approximation of the Stokes problem by residual-free macro bubbles. East-West J. Numer. Math. 4, 265–278
  • 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, 1785–1800