Mixed hp finite element methods for Stokes and non-Newtonian flow

Computer Methods in Applied Mechanics and Engineering

Volumn 175, Issue 3-4, 1999, Pages 217-241

  Schwab, C ^a   Suri, M ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; NON NEWTONIAN FLOW; POLYNOMIALS; STRESS ANALYSIS; VISCOELASTICITY;

ELASTIC-VISCOUS SPLIT STRESS (EVSS) METHOD;

COMPUTATIONAL FLUID DYNAMICS;

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; NON-NEWTONIAN FLOW; STOKES FLOW;

EID: 0033516441     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00355-7     Document Type: Article

References (36)

1. [1] I. Babuška and B.Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. Part I and II, SIAM J. Math. Anal. 19 (1988) 172-203; and 20 (1989) 763-781.
2. [1] I. Babuška and B.Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. Part I and II, SIAM J. Math. Anal. 19 (1988) 172-203; and 20 (1989) 763-781.
3. [2] C. Bernardi and Y. Maday, Approximations Spectrales de Problèmes aux Limites Elliptiques (Springer Verlag, Paris, 1992).
4. [3] C. Bernardi and Y. Maday, Uniform inf-sup conditions for the spectral discretization of the Stokes problem, Preprint, 1997, Math. Models Methods Appl. Sci., to appear.
5. [4] E. Boillat, On the right inverse of the divergence operator in spaces of continuous, piecewise polynomials. Preprint 1995, Dept. of Mathematics, EPFL, Math. Methods Models Appl. Sci., in press.
6. [5] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer Verlag, Heidelberg 1991).
7. [6] L.K. Chilton. Locking-free mixed hp finite element methods for linear and geometrically non-linear elasticity Ph.D. Dissertation, Department of Mathematics and Statistics, UMBC, Baltimore, MD, 1997.
8. [7] L.K. Chilton and M. Suri, On the selection of a locking-free hp element for elasticity problems, Int. J. Numer. Methods Engrg. 40 (1997) 2045-2062.
9. [8] M.J. Crochet and J.M. Marchai, A new mixed finite element for calculating viscoelastic flows, J. Non-Newt. Fluid Mech. 26 (1987) 77-114.
10. [9] L. Demkowicz, K. Gerdes, C. Schwab, A. Bajer and T. Walsh, HP90: A general & flexible hp-FE code in Fortran 90, Comput. Visualization Sci., in press.
11. [10] M. Fortin and R. Pierre, On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows. CMAME 73 (1989) 341-350.
12. [11] M. Fortin and R. Guenette, A new mixed finite element method for computing viscoelastic flows, JNNFM 60 (1995) 27-52.
13. [12] M. Fortin, R. Guenette and R. Pierre, Numerical analysis of the modified EVSS method, Preprint Dept. Math., Univ. Laval, Quebec, 1996.
14. [13] L. Franca, T. Hughes and R. Stenberg, in: M. Gunzburger and R. Nicolardes, eds., Incompressible Computational Fluid Dynamics (Cambridge University Press, 1993).
15. [14] V. Girault and P.A. Raviart, Finite Elements for Navier-Stokes Equations (Springer-Verlag, 1986).
16. [15] B. Gui and I. Babuška, The h-, p-and hp-FEM, Numer. Math. 49 (1985) 577-683.
17. [16] B.Q. Guo and I. Babuška, The hp-version of the FEM I: The basic approximation results, II: Further results and applications, Comput. Mech. 1 (1986) 21-41 and 203-220.
18. [17] B.Q. Guo and I. Babuška, On the regularity of elasticity problems with piecewise analytic data, Adv. Appl. Math. 14 (1993) 307-347.
19. [18] B.Q. Guo and C. Schwab, Regularity of Boundary Value Problems of hydrodynamics in countable normed spaces, in preparation.
20. [19] B. Khomami, K.K. Talwar and H.K. Ganpule, A comparative study of higher- and lower-order finite element techniques for computation of viscoelastic flows, J. Rheol. 38(2) (1994) 255-289.
21. [20] B. Khomami, personal communication, 1996.
22. [21] V.A. Kozlov, V.G. Maz'ya and C. Schwab, On singularities of solutions to the Dirichlet Problem of hydrodynamics near the vertex of a cone, J. reine angew. Math. 456 (1994) 65-97.
23. [22] G.G. Lipscomb, R. Keunings and M.M. Demkovicz, Implication of boundary singularities in complex geometries. J. Non-Newt. Fluid Mech. 24 (1987) 85-96.
24. [23] V.G. Maz'ya and B.A. Plamenevskii, The first boundary value problem for the classical equations of mathematical physics on piecewise smooth domains, Parts I and II, Z. Anal. Anw. 2 (1983) 335-359 and 523-551.
25. [24] R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems, SIAM J. Numer. Anal. 19 (1982) 349-357.
26. [25] E.T. Olsen and J. Douglas Jr., Bounds on spectral condition numbers of matrices arising in the p-version of the FEM, Numer. Math. 69 (1995) 333-352.
27. [26] M. Orlt, Doctoral Dissertation, Stuttgart University, 1998.
28. [27] D. Rajagopalan, R.A. Brown and R.C. Armstrong, Finite Element Methods for calculation of steady viscoelastic flow using constitutive equations with a Newtonian viscosity, J. Non-Newt. Fluid Mech. 36 (1990) 159-199.
29. [28] D. Schötzau, hp-DGFEM for Parabolic Evolution Problems, Doctoral Dissertation, ETH Zürich, to appear.
30. [29] D. Schötzau, C. Schwab and R. Stenberg, Mixed hp FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes, Research Report 97-14, Seminar für Angewandte Mathematik, ETH Zürich, 1997.
31. [30] C. Schwab, p-and hp-FEM (Oxford University Press, 1998).
32. [31] R. Stenberg, Error analysis of some FEM for the Stokes problem, Math. Comp. 54 (1990) 495-508.
33. [32] R. Stenberg and M. Suri, hp-Mixed FEM for elasticity and Stokes flow, Numer. Math. 72 (1996) 367-389.
34. [33] K.K. Talwar, H.K. Ganpule and B. Khomami, A note on selection of spaces in computation of viscoelastic flows using the hp-FEM, J. Non-Newt. Fluid Mech. 52 (1994) 293-307.
35. [34] K.K. Talwar and B. Khomami, Accuracy and convergence of the p-and hp-type FEM for the Stokes and Navier-Stokes equation, AICHE J. 38(1) (1992) 83-91.
36. [35] F. Yurun and M.J. Crochet, High-order finite element methods for steady viscoelastic flows, J. Non-Newt. Fluid Mech. 57 (1995) 283-311.