Table of Contents Author Guidelines Submit a Manuscript
Differential Equations and Nonlinear Mechanics
Volume 2008, Article ID 267454, 21 pages
http://dx.doi.org/10.1155/2008/267454
Research Article

Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019, USA

Received 4 March 2008; Revised 9 July 2008; Accepted 5 September 2008

Academic Editor: Emmanuele Di Benedetto

Copyright © 2008 Rajeev Kumar and Brian H. Dennis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B.-N. Jiang, The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Scientific Computation, Springer, Berlin, Germany, 1998. View at Zentralblatt MATH · View at MathSciNet
  2. I. Christie, D. F. Griffiths, A. R. Mitchell, and O. C. Zienkiewicz, “Finite element methods for second order differential equations with significant first derivatives,” International Journal for Numerical Methods in Engineering, vol. 10, no. 6, pp. 1389–1396, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. J. Westerink and D. Shea, “Consistent higher degree Petrov-Galerkin methods for the solution of the transient convection-diffusion equation,” International Journal for Numerical Methods in Engineering, vol. 28, no. 5, pp. 1077–1101, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. N. Brooks and T. J. R. Hughes, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations,” Computer Methods in Applied Mechanics and Engineering, vol. 32, no. 1–3, pp. 199–259, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Donea, “A Taylor-Galerkin method for convective transport problems,” International Journal for Numerical Methods in Engineering, vol. 20, no. 1, pp. 101–119, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. B.-N. Jiang and L. A. Povinelli, “Least-squares finite element method for fluid dynamics,” Computer Methods in Applied Mechanics and Engineering, vol. 81, no. 1, pp. 13–37, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B.-N. Jiang, T. L. Lin, and L. A. Povinelli, “Large-scale computation of incompressible viscous flow by least-squares finite element method,” Computer Methods in Applied Mechanics and Engineering, vol. 114, no. 3-4, pp. 213–231, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Donea and L. Quartapelle, “An introduction to finite element methods for transient advection problems,” Computer Methods in Applied Mechanics and Engineering, vol. 95, no. 2, pp. 169–203, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. F. Carey and B.-N. Jiang, “Least-squares finite elements for first-order hyperbolic systems,” International Journal for Numerical Methods in Engineering, vol. 26, no. 1, pp. 81–93, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. W. Li, “Least-squares characteristics and finite elements for advection-dispersion simulation,” International Journal for Numerical Methods in Engineering, vol. 29, no. 6, pp. 1343–1358, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. N.-S. Park and J. A. Liggett, “Taylor-least-squares finite element for two-dimensional advection-dominated unsteady advection-diffusion problems,” International Journal for Numerical Methods in Fluids, vol. 11, no. 1, pp. 21–38, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. N.-S. Park and J. A. Liggett, “Application of Taylor-least squares finite element to three-dimensional advection-diffusion equation,” International Journal for Numerical Methods in Fluids, vol. 13, no. 6, pp. 759–773, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. Nguyen and J. Reynen, “A space-time least-square finite element scheme for advection-diffusion equations,” Computer Methods in Applied Mechanics and Engineering, vol. 42, no. 3, pp. 331–342, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. T. J. R. Hughes, L. P. Franca, and G. M. Hulbert, “A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations,” Computer Methods in Applied Mechanics and Engineering, vol. 73, no. 2, pp. 173–189, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. S. Surana and J. S. Sandhu, “Investigation of diffusion in p-version ‘LSFE’ and ‘STLSFE’ formulations,” Computational Mechanics, vol. 16, no. 3, pp. 151–169, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. C. Baiocchi, F. Brezzi, and L. P. Franca, “Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.),” Computer Methods in Applied Mechanics and Engineering, vol. 105, no. 1, pp. 125–141, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. F. Brezzi, L. P. Franca, and A. Russo, “Further considerations on residual-free bubbles for advective-diffusive equations,” Computer Methods in Applied Mechanics and Engineering, vol. 166, no. 1-2, pp. 25–33, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. L. P. Franca, A. Nesliturk, and M. Stynes, “On the stability of residual-free bubbles for convection-diffusion problems and their approximation by a two-level finite element method,” Computer Methods in Applied Mechanics and Engineering, vol. 166, no. 1-2, pp. 35–49, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. G. E. Karniadakis and S. J. Sherwin, Spectral/hp Element Methods for CFD, Numerical Mathematics and Scientific Computation, Oxford University Press, New York, NY, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  20. J. Donea and A. Huerta, Finite Element Methods for Flow Problems, John Wiley & Sons, Chichester, UK, 2003.
  21. C.-C. Yu and J. C. Heinrich, “Petrov-Galerkin method for multidimensional, time-dependent, convective-diffusion equations,” International Journal for Numerical Methods in Engineering, vol. 24, no. 11, pp. 2201–2215, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH