Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 2
72
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Two-level stabilized nonconforming finite element algorithms for the conduction–convection equations

, , &
Pages 152-169 | Received 21 Apr 2017, Accepted 07 Jul 2017, Published online: 18 Aug 2017

References

  • J. Boland and W. Layton, An Analysis of the Finite Element Method for Natural Convection Problems, Numer. Method. Part. Differ. Eq., vol. 2, pp. 115–126, 1990.
  • J. Boland and W. Layton, Error Analysis for Finite Element Methods for Steady Natural Convection Problems, Numer. Funct. Anal. Optim., vol. 11, pp. 449–483, 1990.
  • A. Çıbık and S. Kaya, A Projection-Based Stabilized Finite Element Method for Steady-State Natural Convection Problem, J. Math. Anal. Appl., vol. 381, pp. 469–484, 2011.
  • Z. Luo, J. Chen, I. Navon, and J. Zhu, An Optimizing Reduced PLSMFE Formulation for Non-stationary Conduction–Convection Problems, Int. J. Numer. Methods Fluids, vol. 60, pp. 409–436, 2009.
  • D. Shi and J. Ren, A Least Squares Galerkin–Petrov Nonconforming Mixed Finite Element Method for the Stationary Conduction–Convection Problem, Nonlinear Anal., vol. 72, pp. 1653–1667, 2010.
  • D. Shi and J. Ren, Nonconforming Mixed Finite Element Approximation to the Stationary Navier–Stokes Equations on Anisotropic Meshes, Nonlinear Anal., vol. 71 (2009), pp. 3842–3852, 2009.
  • M. Manzari, An Explicit Finite Element Algorithm for Convection Heat Transfer Problems, Int. J. Numer. Methods Heat Fluid Flow., vol. 9, pp. 860–877, 1999.
  • P. Huang, X. Feng, and Y. He, A Quadratic Equal-Order Stabilized Finite Element Method for the Conduction–Convection Equations, Comput. Fluids., vol. 86, pp. 169–176, 2013.
  • P. Huang, T. Zhang, and Z. Si, A Stabilized Oseen Iterative Finite Element Method for Stationary Conduction–Convection Equations, Math. Meth. Appl. Sci., vol. 35, pp. 103–118, 2012.
  • Z. Weng, X. Feng, and D. Liu, A Fully Discrete Stabilized Mixed Finite Element Method for Parabolic Problems, Numer. Heat Trans. A-Appl., vol. 63, pp. 755–775, 2013.
  • P. Bochev, C. Dohrmann, and M. Gunzburger, Stabilization of Low-Order Mixed Finite Elements for the Stokes Equations, SIAM J. Numer. Anal., vol. 44, pp. 82–101, 2006.
  • S. Ayhn, Two-Level Finite Element Method with a Stabilizing Subgrid for the Natural Convenction Flow Simulation in Different Geometries, Numer. Heat Trans. A-Appl., vol. 59, pp. 799–813, 2011.
  • W. Layton and L. Tobiska, A Two-Level Method with Backtracking for the Navier–Stokes Equations, SIAM J. Numer. Anal., vol. 35, pp. 2035–2054, 1998.
  • W. Layton, A Two Level Discretization Method for the Navier–Stokes, Comput. Math. Appl., vol. 26, pp. 33–38, 1993.
  • J. Xu, A Novel Two-Grid Method for Semilinear Elliptic Equations, SIAM J. Sci. Comput., vol. 15, pp. 231–237, 1994.
  • V. Erivin, W. Layton, and J. Maubach, A Posteriori Error Estimators for a Two-Level Finite Element Method for the Navier–Stokes Equations, Numer. Method. Part. Differ. Eq., vol. 12, pp. 333–346, 1996.
  • Y. He and K. Li, Two-Level Stabilized Finite Element Methods for the Steady Navier–Stokes Problem, Computing, vol. 74, pp. 337–351, 2005.
  • Z. Luo, Theory Bases and Applications of Mixed Finite Element Methods. Science Press, Beijing, 2006 (in Chinese).
  • J. Li and Z. Chen, A New Local Stabilized Nonconforming Finite Element Method for the Stokes Equations, Computing, vol. 82, pp. 157–170, 2008.
  • L. Zhu and Z. Chen, A Two-Level Stabilized Nonnconformiing Finite Element Method for the Stationary Navier–Stokes Equations, Math. Comput. Simul., vol. 5938, pp. 579–585, 2010.
  • P. Huang, J. Zhao, and X. Feng, An Oseen Scheme for the Conduction–Convection Equations Based on a Stabilized Nonconforming Method, Appl. Math. Model., vol. 38, pp. 535–547, 2014.
  • X. Ye, Superconvergence of Nonconforming Finite Element Method for the Stokes Equations, Numer. Method. Part. Differ. Eq., vol. 18, pp. 143–154, 2002.
  • Z. Cai, J. Douglas, and X. Ye, A Stable Nonconforming Quadrilateral Finite Element Method for the Stationary Stokes and Navier–Stokes Equations, Calcolo, vol. 36, pp. 215–232, 1999.
  • H. Su, D. Gui, P. Huang, and X. Feng, Two-level Stabilized Nonconforming Finite Element Algorithms for the Stationary Conduction–Convection Equations, Numer. Heat Trans Part B, vol. 66, pp. 220–223, 2014.
  • Y. Zhang, Y. Hou, and H. Zuo, A Posteriori Error Estimation and Adaptive Computation of Conduction Convection Problems, Appl. Math. Model., vol. 35, pp. 2336–2347, 2011.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.