Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Extension theorems for plate elements with applications
HTML articles powered by AMS MathViewer

by Jinsheng Gu and Xiancheng Hu PDF
Math. Comp. 66 (1997), 1375-1388 Request permission

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
  • Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
  • 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.
  • D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér. 19 (1985), no. 1, 7–32 (English, with French summary). MR 813687, DOI 10.1051/m2an/1985190100071
  • S.C. Brenner, A two–level additive Schwarz preconditioner for nonconforming plate elements, Numer. Math. 72(1996), 419–447.
  • Tony F. Chan, Weinan E, and Jia Chang Sun, Domain decomposition interface preconditioners for fourth-order elliptic problems, Appl. Numer. Math. 8 (1991), no. 4-5, 317–331. MR 1136830, DOI 10.1016/0168-9274(91)90072-8
  • Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
  • Monique Dauge, Elliptic boundary value problems on corner domains, Lecture Notes in Mathematics, vol. 1341, Springer-Verlag, Berlin, 1988. Smoothness and asymptotics of solutions. MR 961439, DOI 10.1007/BFb0086682
  • 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.
  • P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683
  • J. Gu, Domain Decomposition Methods with Nonconforming Finite Elements, Ph.D. thesis (in Chinese), Dept. of Applied Math., Tsinghua University, China, 1994.
  • J. Gu and X. Hu, On domain decomposition methods in two–subdomain nonoverlap cases, Chinese J. Num. Math. & Appl. 17:1(1995), 78–94.
  • Jin Sheng Gu and Xian Cheng Hu, On an essential estimate in the analysis of domain decomposition methods, J. Comput. Math. 12 (1994), no. 2, 132–137. MR 1276427
  • —, Some estimates with nonconforming finite elements in domain decomposition analysis, J. Comput. Math. 15:3(1997).
  • J. Gu and X. Hu, Trace averaging domain decomposition method with nonconforming finite elements, J. Comput. Math. 14 (1996), no. 1, 40–53. MR 1375148
  • P. Lascaux and P. Lesaint, Some nonconforming finite elements for the plate bending problem, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér. 9 (1975), no. R-1, 9–53 (English, with French summary). MR 423968, DOI 10.1051/m2an/197509R100091
  • J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth. MR 0350177
  • L. D. Marini and A. Quarteroni, A relaxation procedure for domain decomposition methods using finite elements, Numer. Math. 55 (1989), no. 5, 575–598. MR 998911, DOI 10.1007/BF01398917
  • L.S.D. Morley, The triangular equilibrium problem in the solution of plate bending problems, Aero. Quart. 19(1968), 149–169.
  • Jindřich Nečas, Les méthodes directes en théorie des équations elliptiques, Masson et Cie, Éditeurs, Paris; Academia, Éditeurs, Prague, 1967 (French). MR 0227584
  • P. Oswald, Hierarchical conforming finite element methods for the biharmonic equation, SIAM J. Numer. Anal. 29 (1992), no. 6, 1610–1625. MR 1191139, DOI 10.1137/0729093
  • Zhong Ci Shi, Error estimates for the Morley element, Math. Numer. Sinica 12 (1990), no. 2, 113–118 (Chinese, with English summary); English transl., Chinese J. Numer. Math. Appl. 12 (1990), no. 3, 102–108. MR 1070298
  • Friedrich Stummel, Basic compactness properties of nonconforming and hybrid finite element spaces, RAIRO Anal. Numér. 14 (1980), no. 1, 81–115 (English, with French summary). MR 566091, DOI 10.1051/m2an/1980140100811
  • 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.
  • 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.
  • 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.
  • Xuejun Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput. 15 (1994), no. 3, 621–644. Iterative methods in numerical linear algebra (Copper Mountain Resort, CO, 1992). MR 1273156, DOI 10.1137/0915041
  • Xuejun Zhang, Two-level Schwarz methods for the biharmonic problem discretized conforming $C^1$ elements, SIAM J. Numer. Anal. 33 (1996), no. 2, 555–570. MR 1388488, DOI 10.1137/0733029
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (1991): 65F10, 65N30
  • Retrieve articles in all journals with MSC (1991): 65F10, 65N30
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
  • 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 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 1375-1388
  • MSC (1991): Primary 65F10, 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-97-00903-4
  • MathSciNet review: 1434939