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Spectral Method for Fourth-Order Problems on Quadrilaterals

Zeitschrift:: Journal of Scientific Computing > Ausgabe 2/2016

Autoren:: Xu-hong Yu, Ben-yu Guo

Wichtige Hinweise

This work is supported in part by NSF of China N.11171227 and N.11426155, Fund for Doctoral Authority of China N.20123127110001, Fund for E-institute of Shanghai Universities N.E03004, Leading Academic Discipline Project of Shanghai Municipal Education Commission N.J50101, and the Hujiang Foundation of China (B14005).

Abstract

In this paper, we investigate the spectral method for fourth-order problems defined on quadrilaterals. Some results on the Legendre irrational orthogonal approximations are established, which play important roles in the related spectral method on quadrilaterals. As examples of applications, we provide spectral schemes for a model problem with various boundary conditions. The spectral accuracy of suggested algorithms are proved. Numerical results demonstrate the effectiveness of suggested algorithms, and confirm the analysis well. The approximation results and techniques developed in this paper are also applicable to other fourth-order problems defined on quadrilaterals.

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Belhachmi, Z., Bernardi, C., Karageorghis, A.: Spectral element discretization of the circular driven cavity, part II: the bilaplacian equation. SIAM J. Numer. Anal. 38, 1926–1960 (2001) CrossRefMathSciNetMATH

Bernardi, C., Maday, Y.: Spectral methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, pp. 209–486. Elsevier, Amsterdam (1997)

Bernardi, C., Maday, Y., Rapetti, F.: Discretisations Variationnelles de Problemes aux Limites Elliptique, Collection: Mathematique et Applications, vol. 45. Springer, Berlin (2004)

Bert, C.W.: Nonlinear vibration of a rectangular plate arbitrary laminated of anisotropic materials. J. Appl. Mech. 40, 425–458 (1973)

Bialecki, B., Karageorghis, A.: A Legendre spectral Galerkin method for the biharmonic Dirichlet problem. SIAM J. Sci. Comput. 22, 1549–1569 (2000) CrossRefMathSciNetMATH

Bjørstad, P.E., Tjøstheim, B.P.: Efficient algorithms for solving a fourth-order equation with spectral-Galerkin method. SIAM J. Sci. Comput 18, 621–632 (1997) CrossRefMathSciNet

Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods, 3rd edn. Springer, Berlin (2008) CrossRefMATH

Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods. Springer, Berlin (2006) MATH

Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Evolution to complex Geometries and Applications to Fluid Dynamics. Springer, Berlin (2007)

10.

Chia, C.Y.: Nonlinear Analysis of Plates. McGraw-Hill, New York (1980)

11.

Doha, E.H., Bhrawy, A.H.: Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials. Appl. Numer. Math. 58, 1224–1244 (2008) CrossRefMathSciNetMATH

12.

Funaro, D.: Polynomial Approxiamtions of Differential Equations. Springer, Berlin (1992)

13.

Guo, B.-Y.: Spectral Methods and Their Applications. World Scientific, Singapore (1998) CrossRefMATH

14.

Guo, B.-Y.: Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations. J. Math. Anal. Appl. 243, 373–408 (2000) CrossRefMathSciNetMATH

15.

Guo, B.-Y.: Some progress in spectral methods. Sci. China Math. 56, 2411–2438 (2013) CrossRefMathSciNetMATH

16.

Guo, B.-Y., Jia, H.-L.: Spectral method on quadrilaterals. Math. Comput. 79, 2237–2264 (2010) CrossRefMathSciNetMATH

17.

Guo, B.-Y., Shen, J., Wang, L.-L.: Optimal spectral-Galerkin methods using generalized Jacobi polynomials. J. Sci. Comput. 27, 305–322 (2006) CrossRefMathSciNetMATH

18.

Guo, B.-Y., Sun, T., Zhang, C.: Jacobi and Laguerre quasi-orthogonal approximations and related interpolations. Math. Comput. 82, 413–441 (2013) MathSciNetMATH

19.

Guo, B.-Y., Wang, L.-L.: Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces. J. Approx. Theory 128, 1–41 (2004) CrossRefMathSciNetMATH

20.

Guo, B.-Y., Wang, L.-L.: Error analysis of spectral method on a triangle. Adv. Comput. Math. 26, 473–496 (2007) CrossRefMathSciNetMATH

21.

Guo, B.-Y., Wang, T.-J.: Composite Laguerre-Legendre spectral method for fourth-order exterior problems. J. Sci. Comput. 44, 255–285 (2010) CrossRefMathSciNetMATH

22.

Guo, B.-Y., Wang, Z.-Q., Wan, Z.-S., Chu, D.-L.: Second order Jacobi approximation with applications to fourth-order differential equations. Appl. Numer. Math. 55, 480–520 (2005) CrossRefMathSciNetMATH

23.

Harras, B., Benamar, R., White, R.G.: Investigation of nonlinear free vibrations of fully clamped symmetrically laminated carbon-fibre-reinforced PEEK(AS4/APC2) rectangular composite panels. Compos. Sci. Technol. 62, 719–727 (2002) CrossRef

24.

Jia, H.-L., Guo, B.-Y.: Petrov–Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons. Chin. Ann. Math. 31B, 855–878 (2010) CrossRefMathSciNet

25.

Karniadakis, G.E., Sherwin, S.J.: Spectral/hp Element Methods for CFD, 2nd edn. Oxford University Press, Oxford (2005) CrossRef

26.

Narita, Y.: Combinations for the free-vibration behaviors of anisotropic rectangular plates under general edge conditions. J. Appl. Mech. 67, 568–573 (2000) CrossRefMATH

27.

Reddy, J.N.: A simply higher-order theory for laminated composite plates. J. Appl. Mech. 51, 745–754 (1984) CrossRefMATH

28.

Shen, J., Tang, T., Wang, L.-L.: Spectral Methods: Algorithms, Analysis and Applications. Springer, Berlin (2011) CrossRef

29.

Yu, X.-H., Guo, B.-Y.: Spectral element method for mixed inhomogeneous boundary value problems of fourth order. J. Sci. Comput. 61, 673–701 (2014) CrossRefMathSciNetMATH

Titel: Spectral Method for Fourth-Order Problems on Quadrilaterals
Autoren:: Xu-hong Yu
Ben-yu Guo
Publikationsdatum: 29.04.2015
DOI: https://doi.org/10.1007/s10915-015-0031-6
Verlag: Springer US
Zeitschrift: Journal of Scientific Computing
Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691

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