New approaches to error estimation and adaptivity for the Stokes and Oseen equations

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 1, 1999, Pages 3-15

  Oden, J T ^a   Prudhomme, S ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Error estimation; Finite element solutions; Stokes and Oseen equations

Indexed keywords

ERROR; FINITE ELEMENT ANALYSIS; STOKES FLOW;

ERROR CORRECTION; FINITE ELEMENT METHOD; STOKES FORMULA;

EID: 0032694896     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19990915)31:1<3::aid-fld952>3.0.co;2-b     Document Type: Article

References (15)

1. I. Babuška, T. Strouboulis, CS. Upadhyay and S.K. Gangaraj, 'A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method', Int. J. Numer. Methods Eng., 38, 4207-4235 (1995).
2. R. Becker and R. Rannacher, 'Weighted a posteriori error control in FE method', in ENUMATH-95, Paris, September, 1995.
3. M. Paraschivoiu, J. Peraire and A.T. Patera, 'A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations', Comp. Methods Appl. Mech. Eng., 150, 289-312 (1997).
4. J.T. Oden and S. Prudhomme, 'A technique for a posteriori error estimation of h-p approximations of the Stokes equations', in P. Ladevèze and J.T. Oden (eds), Advances in Adaptive Computational Methods in Mechanics, Elsevier, Amsterdam, 1998, pp. 43-63.
5. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986.
6. L. Demkowicz, J.T. Oden, W. Rachowicz and O. Hardy, 'Toward a universal h-p adaptive finite element strategy. Part 1. Constrained approximation and data structure', Comp. Methods Appl. Mech. Eng., 77, 113-180 (1989).
7. R.E. Bank, 'Hierarchical bases and the finite element method', Acta Numerica, 5, 1-43 (1996).
8. J.T. Oden, 'Optimal h-p finite clement methods', Comp. Methods Appl. Mech. Eng., 112, 309-331 (1994).
9. B. Szabó and I. Babuška, Finite Element Analysis, John Wiley & Sons, New York, 1991.
10. M. Ainsworth and J.T. Oden, 'A unified approach to a posteriori error estimation using element residual methods', Numer. Math., 65, 23-50 (1993).
11. M. Ainsworth and J.T. Oden, 'A posteiori error estimation in finite element analysis', Comput. Methods Appl. Mech. Eng., 142, 1-88 (1997).
12. P. Ladevèze and D. Leguillon, 'Error estimate procedure in the finite element method and applications', SIAM J. Numer. Anal., 20, 485-509 (1983).
13. M. Paraschivoiu and A.T. Patera, 'A posteriori bounds for linear-functional outputs of Crouzeix-Raviart finite element discretizations of the incompressible Stokes problem', preprint.
14. J. Simo and F. Armero, 'Unconditional stability and long-term behavior of the transient algorithms for the incompressible Navier-Stokes and Euler equations', Comp. Methods Appl. Mech. Eng., 111, 111-154 (1994).
15. V.P. Fragos, S.P. Psychoudaki and N.A. Malamataris, 'Computer-aided analysis of flow past a surface-mounted obstacle', Int. J. Numer. Methods Fluids, 25, 495-512 (1997).