The hp-Mortar Finite-Element Method for the Mixed Elasticity and Stokes Problems

Computers and Mathematics with Applications

Volumn 46, Issue 1, 2003, Pages 35-55

  Ben Belgacem, F ^a   Chilton, L K ^b   Seshaiyer, P ^c  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

^c TEXAS TECH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; PROBLEM SOLVING; THEOREM PROVING;

STOKES PROBLEMS;

ELASTICITY;

EID: 0041823226     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)90079-4     Document Type: Conference Paper

References (39)

1. L. Pavarino and O. Widlund, Iterative substructuring methods for spectral element discretizations of elliptic systems. II: Mixed methods for linear elasticity and Stokes flow, SIAM J. Num. Anal. 37, 375-402, (1999).
2. I. Babuška and M. Suri, The p and h-p-versions of the finite element method: Basic principles and properties, SIAM Review 36, 578-632, (1994).
3. I. Babuška and M. Suri, The optimal convergence rate of the p-version of the finite element method, SIAM J. Num. Anal. 24, 750-776, (1987).
4. B. Szabó and I. Babuška, Finite Element Analysis, John Wiley & Sons, New York, (1991).
5. W. Gui and I. Babuška, The h, p and h-p-version of the finite element method in one dimension, Part 1, Num. Math. 49, 577-612, (1986).
6. W. Gui and I. Babuška, The h, p and h-p-version of the finite element method in one dimension, Part 2, Num. Math. 49, 613-657, (1986).
7. W. Gui and I. Babuška, The h, p and h-p-version of the finite element method in one dimension, Part 3, Num. Math. 49, 659-683, (1986).
8. C. Bernardi, Y. Maday and A.T. Patera, A new non conforming approach to domain decomposition: The mortar element method, In Collège de France Seminar, (Edited by H. Brezis and J.-L. Lions), Pitman, (1990).
9. P. Seshaiyer and M. Suri, Uniform h-p convergence results for the mortar finite element method, Math. Comp. 69, 521-546, (2000).
10. F. Ben Belgacem, Discrétisations 3D nonconformes par la méthode de décomposition de domaines des éléments avec joints: Analyse mathématique et mise en oeuvre pour le problème de Poisson, Ph.D. Thesis, Université Pierre et Marie Curie, Paris, France, Note technique EDF, Ref. HI72/93017, (1993).
11. P. Seshaiyer and M. Suri, h-p-meshing via non-conforming finite element methods, Comp. Methods Appl. Mech. Eng. 189, 1011-1030, (2000).
12. F. Ben Belgacem, P. Seshaiyer and M. Suri, Optimal convergence rates of hp mortar finite element methods for second order elliptic problems, Modél. Math. et Anal. Numér. 34, 591-608, (2000).
13. C. Bernardi, M. Dauge and Y. Maday, Interpolation of nullspaces for polynomial approximation of divergence-free functions in a cube, In Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, Volume 167, (Edited by M. Costabel, M. Dauge and S. Nicaise), pp. 27-46, Dekker, (1994).
14. F. Ben Belgacem, The mixed mortar finite element method for the incompressible Stokes equations: Convergence analysis, SIAM J. Num. Anal. 37, 1085-1100, (2000).
15. F. Ben Belgacem, C. Bernardi, N. Chorfi and Y. Maday, Inf-sup condition for the mortar spectral element discretization for the Stokes problem, Num. Math. 85, 257-281, (2000).
16. K.J. Arrow, L. Hurwicz and H. Uzawa, Studies of Linear and Nonlinear Programming, Stanford University Press, Stanford, CA, (1958).
17. A. Klawonn, An optimal preconditioner for a class of saddle point problems with a penalty term, SIAM J. Sci. Comput. 19, 540-552, (1998).
18. L. Pavarino and O. Widlund, Iterative substructuring methods for spectral element discretizations of elliptic systems. I: Compressible linear elasticity, SIAM J. Num. Anal. 37, 353-374, (1999).
19. D.A. Adams, Sobolev Spaces, Academic Press, New York, (1975).
20. P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, Volume 24, Pitman, (1985).
21. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Volume 15, Springer-Verlag, New York, (1991).
22. P.-G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, (1978).
23. I. Babuška and M. Suri, Locking effects in the finite element approximation of elasticity problem, Num. Math. 62, 439-463, (1992).
24. M. Suri, Analytic and computational assessment of locking in the hp-finite element, Comp. Methods Appl. Mech. Eng. 133, 347-371, (1996).
25. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, (1986).
26. D. Silver and A. Wathen, Fast iterative solution of stabilized Stokes problem, Part 2: Using general block preconditioned, SIAM J. Num. Anal. 31, 1352-1367, (1994).
27. C. Bernardi and Y. Maday, Uniform inf-sup conditions for the spectral discretization of the Stokes problem, Math. Mod. Meth. Appl. Sci. 49, 395-414, (1999).
28. L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, Modél. Math, et Anal. Numér. 19, 111-143, (1985).
29. 2-projection on finite element function spaces, Math. Compu. 48, 521-532, (1987).
30. J. Boland and R. Nicolaides, Stability of finite element under divergence constraints, SIAM J. Num. Anal. 20, 722-731, (1983).
31. C. Bernardi and Y. Maday, Spectral methods, In Handbook of Numerical Analysis, Volume V, (Edited by P.G. Ciarlet and J.L. Lions), North-Holland, (1997).
32. C. Bernardi and V. Girault, A local regularization operator for triangular and quadrangular finite elements, SIAM J. Num. Anal. 35, 1893-1916, (1998).
33. th France-USSR-Italy Joint Symposium Proceedings, Pavia, pp. 129-163, (1989).
34. R. Stenberg and M. Suri, Mixed finite element methods for problems in elasticity and stokes flows, Num. Math. 72, 367-389, (1986).
35. F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements, Model. Math. Anal. Numér. 31, 289-302, (1997).
36. F. Ben Belgacem, Stabilized domain decomposition method with non-matching grids for three-dimensional finite elements. I. The Poisson problem, (submitted).
37. F. Ben Belgacem, A stabilized domain decomposition method with non-matching grids: The three-dimensional mixed finite elements for the Stokes system, SIAM Journal of Numerical Analysis (to appear).
38. C. Bernardi, Y. Maday and G. Sacchi-Landriani, Non conforming matching conditions for coupling spectral and finite element methods, Appl. Numer. Math. 54, 64-84, (1989).
39. Y. Achdou, Y. Maday and O.B. Widlund, Iterative substructuring preconditioners for the mortar finite element method in two dimensions, SIAM J. Num. Anal. 36, 551-580, (1999).