PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2012 | 10 | 1 | 44-54
Tytuł artykułu

Approximations of the partial derivatives by averaging

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A straightforward generalization of a classical method of averaging is presented and its essential characteristics are discussed. The method constructs high-order approximations of the l-th partial derivatives of smooth functions u in inner vertices a of conformal simplicial triangulations T of bounded polytopic domains in ℝd for arbitrary d ≥ 2. For any k ≥ l ≥ 1, it uses the interpolants of u in the polynomial Lagrange finite element spaces of degree k on the simplices with vertex a only. The high-order accuracy of the resulting approximations is proved to be a consequence of a certain hypothesis and it is illustrated numerically. The method of averaging studied in [Dalík J., Averaging of directional derivatives in vertices of nonobtuse regular triangulations, Numer. Math., 2010, 116(4), 619–644] provides a solution of this problem in the case d = 2, k = l = 1.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
1
Strony
44-54
Opis fizyczny
Daty
wydano
2012-02-01
online
2011-12-09
Twórcy
autor
Bibliografia
  • [1] Ainsworth M., Oden J.T., A Posteriori Error Estimation in Finite Element Analysis, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 2000 http://dx.doi.org/10.1002/9781118032824
  • [2] Ciarlet P.G., The Finite Element Method for Elliptic Problems, Stud. Math. Appl., 4, North Holland, Amsterdam-New York-Oxford, 1978 http://dx.doi.org/10.1016/S0168-2024(08)70178-4
  • [3] Dalík J., Averaging of directional derivatives in vertices of nonobtuse regular triangulations, Numer. Math., 2010, 116(4), 619–644 http://dx.doi.org/10.1007/s00211-010-0316-5
  • [4] Hlaváček I., Křížek M., Pištora V., How to recover the gradient of linear elements on nonuniform triangulations, Appl. Math., 1996, 41(4), 241–267
  • [5] Křížek M., Neittaanmäki P., Superconvergence phenomenon in the finite element method arising from averaging gradients, Numer. Math., 1984, 45(1), 105–116 http://dx.doi.org/10.1007/BF01379664
  • [6] Li S., Concise formulas for the area and volume of a hyperspherical cap, Asian J. Math. Stat., 2011, 4(1), 66–70 http://dx.doi.org/10.3923/ajms.2011.66.70
  • [7] Naga A., Zhang Z., The polynomial-preserving recovery for higher order finite element methods in 2D and 3D, Discrete Contin. Dyn. Syst. Ser. B, 2005, 5(3), 769–798 http://dx.doi.org/10.3934/dcdsb.2005.5.769
  • [8] Quarteroni A., Valli A., Numerical Approximation of Partial Differential Equations, Springer Ser. Comput. Math., 23, Springer, Berlin, 1994
  • [9] Zhang Z., Naga A., A new finite element gradient recovery method: superconvergence property, SIAM J. Sci. Comput. 2005, 26(4), 1192–1213 http://dx.doi.org/10.1137/S1064827503402837
  • [10] Zienkiewicz O.C., Cheung Y.K., The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, London, 1967
  • [11] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimates. Part I: The recovery technique, Internat. J. Numer. Methods Engrg., 1992, 33(7), 1331–1364 http://dx.doi.org/10.1002/nme.1620330702
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0107-y
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.