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Extension theorems for plate elements with applications
Author(s):
Jinsheng
Gu;
Xiancheng
Hu.
Journal:
Math. Comp.
66
(1997),
1375-1388.
MSC (1991):
Primary 65F10, 65N30
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Abstract:
Extension theorems for plate elements are established. Their applications to the analysis of nonoverlapping domain decomposition methods for solving the plate bending problems are presented. Numerical results support our theory.
References:
- 1.
- R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. MR 56:9247
- 2.
- 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), 701-709.
- 3.
- D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, M
 AM. 19(1985), 7-32. MR 87g:65126 - 4.
- S.C. Brenner, A two-level additive Schwarz preconditioner for nonconforming plate elements, Numer. Math. 72(1996), 419-447. CMP 96:08
- 5.
- T.F. Chan, W. E and J. Sun, Domain decomposition interface preconditioners for fourth order elliptic problems, Appl. Numer. Math. 8(1991), 317-331. MR 92g:65125
- 6.
- P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 58:25001
- 7.
- M. Dauge, Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions, Springer-Verlag, New York, 1988. Lecture Notes in Math., Vol.1341. MR 91a:35078
- 8.
- M. Dryja and O.B. Widlund, An additive variant of the Schwarz alternating method in the case of many subregions, Technical Report 339, Dept. of Computer Science, Courant Institute, 1987.
- 9.
- P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985. MR 86m:35044
- 10.
- J. Gu, Domain Decomposition Methods with Nonconforming Finite Elements, Ph.D. thesis (in Chinese), Dept. of Applied Math., Tsinghua University, China, 1994.
- 11.
- J. Gu and X. Hu, On domain decomposition methods in two-subdomain nonoverlap cases, Chinese J. Num. Math. & Appl. 17:1(1995), 78-94.
- 12.
- -, On an essential estimate in the analysis of domain decomposition methods, J. Comput. Math. 12:2(1994), 132-137. MR 95a:65205
- 13.
- -, Some estimates with nonconforming finite elements in domain decomposition analysis, J. Comput. Math. 15:3(1997).
- 14.
- -, Trace averaging domain decomposition method with nonconforming finite elements, J. Comput. Math. 14:1(1996), 40-53. MR 96k:65078
- 15.
- P. Lascaux and P. Lesaint, Some nonconforming finite elements for the plate bending problem, RAIRO. R-1(1975), 9-53. MR 54:11941
- 16.
- J.L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications.I, Grund. B. 181. Berlin, Springer, 1972. MR 50:2670
- 17.
- L.D. Marini and A. Quarteroni, A relaxation procedure for domain decomposition methods using finite elements, Numer. Math. 55(1989), 575-598. MR 90g:65150
- 18.
- L.S.D. Morley, The triangular equilibrium problem in the solution of plate bending problems, Aero. Quart. 19(1968), 149-169.
- 19.
- J. Ne[??]cas, Les Méthodes Directes en Théorie des Équations Elliptiques, Academia, Prague, 1967. MR 37:3168
- 20.
- P. Oswald, Hierarchical conforming finite element methods for the biharmonic equation, SIAM J. Numer. Anal. 29(1992), 1610-1625. MR 93k:65098
- 21.
- Z. Shi, Error estimates for the Morley element, Chinese J. Num. Math. & Appl. 12:3(1990), 102-108. MR 91i:65182
- 22.
- F. Stummel, Basic compactness properties of nonconforming and hybrid finite element spaces, RAIRO Anal. Num. 4:1(1980), 81-115. MR 81h:65058
- 23.
- J. Sun, Multilevel preconditioners for 4th order problems and domain decomposition methods, In Proceedings of the Sixth International Conference on Domain Decomposition, A. Quarteroni et al (eds.) Italy, 1992.
- 24.
- O.B. Widlund, An extension theorem for finite element spaces with three applications, in Numerical Techniques in Continuum Mechanics, Vol.16. Hackbusch. W.(eds). Braaunschweig Wiesbaden, 1987.
- 25.
- X. Zhang, Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem, Ph.D. thesis (Technical Report 584), Courant Institute, New York University, 1991.
- 26.
- -, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput. 15:3(1994), 621-644. MR 96a:65048
- 27.
- -, Two-level Schwarz methods for the biharmonic problem discretized by conforming
 elements, SIAM J. Numer. Anal. 33(1996), 555-570. MR 97b:65133
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Additional Information:
Jinsheng
Gu
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, China
Email:
gjs@mailhost.cnu.edu.cn
Xiancheng
Hu
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing 100084, China
DOI:
10.1090/S0025-5718-97-00903-4
PII:
S 0025-5718(97)00903-4
Keywords:
Extension theorem,
plate element,
domain decomposition
Received by editor(s):
November 22, 1994
Received by editor(s) in revised form:
November 22, 1995 and May 1, 1996
Additional Notes:
This work was supported by the National Natural Science Foundation of China
Copyright of article:
Copyright
1997,
American Mathematical Society
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