zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
High-accuracy analysis of two nonconforming plate elements. (English) Zbl 1155.74045
Summary: We prove the superconvergence of Morley element and the incomplete biquadratic nonconforming element for the plate bending problem. On uniform rectangular meshes, we obtain a superconvergence property at the symmetric points of the elements and a global superconvergent result by a proper postprocessing method.
74S05Finite element methods in solid mechanics
74K20Plates (solid mechanics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
[1]Babuska I., Strouboulis T., Upadhyay C.S., Gangaraj S.K.: Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplaces, Poissons, and the elasticity equations. Numer. Meth. PDEs. 12, 347–392 (1996)
[2]Brandts J.H.: Superconvergence and a posteriori error estimation in triangular mixed finite elements. Numer. Math. 68, 311–324 (1994) · Zbl 0823.65103 · doi:10.1007/s002110050064
[3]Chen C.M.: Superconvergent points of Galerkin’s method for two point boundary value problems. Numer. Math. J. Chinese Univ. 1, 73–79 (1979) (in Chinese)
[4]Chen C.M.: Superconvergence points of bicubic Hermite finite element for the plate bending problem, J. Xiangtan Univ. 2, 73–79 (1979)
[5]Chen C.M., Huang Y.Q.: High Accuracy Theory of Finite Element Methods (in Chinese). Hunan Science Press, People’s Republic of China (1995)
[6]Chen H.S., Li B.: Superconvergence analysis and error expansion for the Wilson nonconforming finite element. Numer. Math. 69, 125–140 (1994) · Zbl 0818.65098 · doi:10.1007/s002110050084
[7]Ciarlet P.G.: The Finite Element method for Elliptic Problems. North-Holland, Amsterdam (1978)
[8]Douglas J. Jr, Dupont T.: Superconvergence for Galerkin methods for the two point boundary problem via local projections. Numer. Math. 21, 270–278 (1973) · Zbl 0281.65046 · doi:10.1007/BF01436631
[9]Ewing R.E., Lazarov R.D., Wang J.: Superconvergence of the velocity along the Gauss lines in mixed finite element methods. SIAM J. Numer. Anal. 28, 1015–1029 (1991) · Zbl 0733.65065 · doi:10.1137/0728054
[10]Křížek M., Neittaanmäki P.: On superconvergence techniques. Acta Appl. Math. 9, 175–198 (1987) · Zbl 0624.65107 · doi:10.1007/BF00047538
[11]Křížek, M., Neittaanmäki, P., Stenberg, R. (eds.): Finite Element Methods: Superconvergence, Post-processing, and A Posteriori Estimates. Lecture Notes in Pure and Applied Mathematics Series, vol. 196. Marcel Dekker, New York (1998)
[12]Li B., Luskin M.: Nonconforming finite element approximation of crystalline microstructures. Math. Comp. 67, 917–946 (1998) · Zbl 0901.73076 · doi:10.1090/S0025-5718-98-00941-7
[13]Lin, Q., Yan, N.N.: The Construction and Analysis for Efficient Finite Elements. Hebei. Univ. Pub. House, in Chinese (1996)
[14]Lin Q., Tobiska L., Zhou A.: On the superconvergence of nonconforming low order finite elements applied to the Poisson equation. IMA J. Numer. Anal. 25, 160–181 (2005) · Zbl 1068.65122 · doi:10.1093/imanum/drh008
[15]Mao S.P., Chen S.C., Sun H.X.: A quadrilateral, anisotropic, superconvergent nonconforming double set parameter element. Appl. Numer. Math. 56, 937–961 (2006) · Zbl 1094.65120 · doi:10.1016/j.apnum.2005.07.005
[16]Mao, S.P., Shi, Z.C.: Superconvergence of a nonconforming P 1 finite element method for the Stokes problem, preprint
[17]Ming P.B., Xu Y., Shi Z.C.: Superconvergence studies of quadrilateral nonconforming rotated Q 1 elements. Int. J. Numer. Anal. Model. 3, 322–332 (2006)
[18]Schatz A.H., Sloan I.H., Wahlbin L.B.: Superconvergence in finite element methods and meshes that are symmetric with respect to a point. SIAM. J. Numer. Anal. 33, 505–521 (1996) · Zbl 0855.65115 · doi:10.1137/0733027
[19]Shi Z.C.: On the convergence of the incomplete biquadratic plate element. Math. Numer. Sinica 8, 53–62 (1986)
[20]Shi Z.C., Chen Q.Y.: A new plate element with high accuracy. Sci. China 30, 504–515 (2000)
[21]Shi Z.C.: The F-E-M-Test for nonconforming finite elements. Math. Comput. 49, 391–405 (1987)
[22]Shi Z.C., Jiang B.: A new superconvergence property of Wilson nonconforming finite element. Numer. math. 78, 259–268 (1997) · Zbl 0897.65063 · doi:10.1007/s002110050312
[23]Shi Z.C.: On the error estimates of Morley’s element. Math. Numer. Sinica (Chinese) 12, 113–118 (1990)
[24]Shi Z.C.: On the accuary of the quasi-conforming and generalized conforming finite elements. China Ann. Math. Ser. B 11, 148–155 (1990)
[25]Shi Z.C., Chen S.C., Huang H.C.: Plate elements with high accuary. In: Li, T.T. (eds) Collec Geom Anal Math Phys, pp. 155–164. World Scientific, Singapore (1997)
[26]Wahlbin L.B.: Superconvergence in Galerkin Finite Element Methods. Lecture Notes in Mathematicas, vol. 1605. Springer, Berlin (1995)
[27]Xu J., Zhang Z.: Analysis of recovery type a posteriori error estimators for mildly structured grids. Math. Comp. 73, 1139–1152 (2004) · Zbl 1050.65103 · doi:10.1090/S0025-5718-03-01600-4
[28]Zhang Z.: Derivative superconvergence points in finite element solutions of Poissons equation for the serendipity and intermediate families: A theoretical justification. Math. Comp. 67, 541–552 (1998) · Zbl 0893.65056 · doi:10.1090/S0025-5718-98-00942-9
[29]Zlamal M.: Some superconvergence results in the finite element method. Lecture Notes in Math., vol. 606, pp. 353–362. Springer, Berlin (1977)
[30]Zlamal M.: Superconvergence and reduced integration in the finite element method. Math. Comp. 32, 663–685 (1978) · Zbl 0448.65068 · doi:10.2307/2006479
[31]Zienkiewicz O.C., Zhu J.Z.: The superconvergence patch recovery and a posteriori error estimates, Part 1: The recovery technique. Int. J. Numer. Methods Eng. 33, 1331–1364 (1992) · Zbl 0769.73084 · doi:10.1002/nme.1620330702
[32]Zienkiewicz O.C., Zhu J.Z.: The superconvergence patch recovery and a posteriori error estimates, Part 2: Error estimates and adaptivity. Int. J. Numer. Methods Eng. 33, 1364–1382 (1992)
[33]Zhu, Q.D., Lin, Q.: Superconvergence theory of the finite element method. Hunan Science Press, Hunan, China (in Chinese) (1989)