Mass- and momentum conservation of the least-squares spectral element method for the stokes problem

Journal of Scientific Computing

Volumn 27, Issue 1-3, 2006, Pages 389-401

  Proot, Michael M J ^a,b   Gerritsma, Marc I ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b SHELL GLOBAL SOLUTIONS INTERNATIONAL B V   (United States)

Author keywords

Least squares; Mass and momentum conservation; Spectral elements; Stokes problem

Indexed keywords

ENERGY CONSERVATION; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; NAVIER STOKES EQUATIONS; SPECTRUM ANALYSIS;

GALERKIN SPECTRAL ELEMENT FORMULATION; MASS- AND MOMENTUM CONSERVATION; SPECTRAL ELEMENTS;

PROBLEM SOLVING;

EID: 33745038997     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-005-9030-3     Document Type: Conference Paper

References (14)

1. Bernardi, C., and Maday, Y. (1992). Approximations Spectrale de Problèmes aux Limites Élliptiques. Springer-Verlag, Paris.
2. Chang, C. L., and Nelson, J. J. (1997). Least-squares finite element method for the Stokes problem with zero residual of mass conservation. SIAM J. Numer. Anal. 34(2), 480-489.
3. Deang, J. M., and Gunzburger, M. D. (1998). Issues related to least-squares finite element methods for the Stokes equations. SIAM J. Sci. Comput. 20(3), 878- 906.
4. Deville, M. O., Fischer, P. F., and Mund, E. H. (2002). High-Order Methods for Incompressible Fluid Flow. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge.
5. Gerritsma, M. I., and Proot, M. M. J. (2002). Analysis of a discontinuous least squares spectral element method. J. Sci. Comput. 17(1-3), 323-333.
6. Karniadakis, G. E., and Sherwin, S. J. (1999). Spectrallhp Element Methods for CFD. Oxford University Press, Oxford.
7. Maday, Y., and Patera, A. T. (1989). Spectral element methods for the incompressible Navier-Stokes equations. In Noor, A. K., and Oden, J. T. (eds.), State-of-tha-Art Surveys in Computational Mechanics, ASME, NY.
8. Nool, M., and Proot, M. M. J. (2002). Parallel implementation of a least-squares spectral element solver for incompressible flow problems. In International Conference on Computational Science, Amsterdam, The Netherlands, April 21-24. Springer.
9. Nool, M., and Proot, M. M. J. (2002). A parallel state-of-the-art least-squares spectral element solver for incompressible flow problems. In VECPAR 2002 Conference on High Performance Computing for Computational Science, Porto, Portugal, June 26-28. Universidade do Porto, Faculdade de Engeuharia.
10. Pontaza, J. P., and Reddy, J. N. (2003). Spectral/hp least squares finite element formulation for the Navier-Stokes equation. J. Comput. Phys. 190(2), 523- 549.
11. Pontaza, J. P., and Reddy, J. N. (2004). Space-time coupled spectral/hp least squares finite element formulation for the incompressible Navier-Stokes equation. J. Comput. Phys. 197(2), 418-459.
12. Proot, M. M. J. (2003). The Least-Squares Spectral Element Method. Theory, Implementation and Application to Incompressible Flows. Ph.D thesis, Delft University of Technology.
13. Proot, M. M. J., and Gerritsma, M. I. (2002). A least-squares spectral element formulation for the Stokes problem. J. Sci. Comput. 17(1-3), 311-322.
14. Proot, M. M. J., and Gerritsma, M. I. (2002). Least-squares spectral elements applied to the Stokes problem. J. Comput. Phys. 181(2), 454-477.