Preconditioning complicated finite elements by simple finite elements

SIAM Journal on Scientific Computing

Volumn 17, Issue 5, 1996, Pages 1269-1274

  Brenner, Susanne C ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Additive Schwarz methods; Finite elements; Preconditioning

Indexed keywords

EID: 0442325317     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594277065     Document Type: Article

References (22)

1. J. H. ARGYRIS, I. FRIED, AND D. W. SCHARPF, The TUBA family of plate elements for the matrix displacement method, Aero. J. Roy. Aero. Soc., 72 (1968), pp. 701-709.
2. R. E. BANK AND T. F. DUPONT, Analysis of a Two-Level Scheme for Solving Finite Element Equations, Tech. report CNA-159, University of Texas at Austin, Center for Numerical Analysis, Austin, TX, 1980.
3. J. H. BRAMBLE, Multigrid Methods, Longman Scientific and Technical, Essex, U.K., 1993.
4. J. H. BRAMBLE, J. E. PASCIAK, AND X. ZHANO, Two-level preconditioned for Im'th order elliptic finite element problems, East-West J. Numer. Math., 1996, to appear.
5. S. C. BRENNER, An optimal-order nonconforming multigrid method for the biharmonic equation, SIAM J. Numer. Anal., 26 (1989). pp. 1124-1138.
6. _, Two-level additive Schwarz preconditioned for nonconforming finite elements, Math. Comp., 65(1996), pp. 897-921.
7. _, A two-level additive Schwarz preconditioner for nonconforming plate elements, Numer. Math., 72(1996), pp. 419-447.
8. S. C. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, Berlin, Heidelberg, 1994.
9. T. F. CHAN AND T. P. MATHEW, Domain decomposition algorithms, in Acta Numerica 1994, A. Iserles, ed., Cambridge University Press, Cambridge, New York, Melbourne, 1994, pp. 61-143.
10. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, New York, Oxford, 1978.
11. R. W. CLOUGH AND J. L. TOCHER, Finite element stiffness matrices for analysis of plates in bending, in Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., OH, 1965, pp. 515-545.
12. M. DRYJA AND O. B. WIDLUND, Some Domain Decomposition Algorithms for Elliptic Problems, Tech. report 438, Department of Computer Science, Courant Institute, New York, 1989.
13. M. GRIEBEL AND P. OSWALD, On the abstract theory of additive and multiplicative Schwarz algorithms, Numer. Math., 70 (1995), pp. 163-180.
14. M. R. HANISCH, Multigrid preconditioning for the biharmonic Dirichlet problem, SIAM J. Numer. Anal., 30 (1993), pp. 184-214.
15. P. L. LIONS, On the Schwarz alternating method, I, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988, pp. 1-42.
16. L. S. D. MORLEY, The triangular equilibrium problem in the solution of plate bending problems, Aero. Quart., 19 (1968), pp. 149-169.
17. 1/2;(S), Soviet J. Numer. Anal. Math. Modelling, 4 (1989), pp. 493-506.
18. _, Fictitious components and subdomain alternating methods, Soviet J. Numer. Anal. Math. Modelling, 5(1990), pp. 53-68.
19. P. OSWALD, Preconditioned for nonconforming elements, Math. Comp., 65 (1996), pp. 923-941.
20. G. SANDER, Bornes supérieures et inférieures dans l'analyse matricielle des plaques en flexion-torsion, Bull. Soc. Roy. Sci. Liège, 33 (1964), pp. 456-494.
21. Z. SHI, On the convergence of the incomplete biquadratic nonconforming plate element, Math. Numer. Sinica, 8 (1986), pp. 53-62. (In Chinese.)
22. J. XU, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, Computing, 1996, to appear.