Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Some spectral approximations of two-dimensional fourth-order problems

Authors: Christine Bernardi, Giuseppe Coppoletta and Yvon Maday
Journal: Math. Comp. 59 (1992), 63-76
MSC: Primary 65N35; Secondary 65D30, 76D05, 76M25
MathSciNet review: 1134714
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with the approximation of the biharmonic equation in a square domain with Dirichlet boundary conditions. Two types of discrete problems are presented, the numerical analysis is performed, and estimates for the error between the exact and approximate solutions are given.

References [Enhancements On Off] (What's this?)

  • [1] C. Bernardi, G. Coppoletta, and Y. Maday, Some spectral approximations of multidimensional fourth-order problems, Internal Report 90021, Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris, 1990.
  • [2] C. Bernardi and Y. Maday, Some spectral approximations of one-dimensional fourth-order problems, Progress in Approximation Theory (P. Nevai and A. Pinkus, eds.), Academic Press, Boston, 1991, pp. 43-116. MR 1114769 (92j:65176)
  • [3] -, Spectral methods, Handbook of Numerical Analysis (P. G. Ciarlet and J.-L. Lions, eds.), North-Holland (to appear).
  • [4] C. Bernardi and G. Raugel, Méthodes d'éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone non convexe, Calcolo 18 (1981), 255-291. MR 647827 (83a:65107)
  • [5] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral methods in fluid dynamics, Springer-Verlag, New York, 1987. MR 917480 (89m:76004)
  • [6] C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp. 38 (1982), 67-86. MR 637287 (82m:41003)
  • [7] P. J. Davis and P. Rabinowitz, Methods of numerical integration, 2nd ed., Academic Press, Orlando, 1984. MR 760629 (86d:65004)
  • [8] D. Funaro and W. Heinrichs, Some results about the pseudospectral approximation of one-dimensional fourth-order problems, Numer. Math. 58 (1990), 399-418. MR 1077586 (91m:65206)
  • [9] L. Gatteschi, Su una formula di quadratura "quasi gaussiana". Tabulazione delle ascisse d'integrazione et delle relative costanti di Christoffel, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 98 (1963-64), 641-661. MR 0166920 (29:4193)
  • [10] P. Grisvard, Elliptic problems in nonsmooth domains, Pitman, Boston, 1985. MR 775683 (86m:35044)
  • [11] E. B. Karpilovskaya, A method of collocation for integro-differential equations with biharmonic principal part, U.S.S.R. Comput. Math. and Math. Phys. 10 (1970), no. 6, 240-246.
  • [12] O. Koutchmy (in preparation).
  • [13] J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vols. 1 and 2, Dunod, Paris, 1968. MR 0247243 (40:512)
  • [14] Y. Maday, Résultats d'approximation optimaux pour les opérateurs d'interpolation polynômiale, C. R. Acad. Sci. Paris Sér. I. 312 (1991), 705-710. MR 1105630 (92d:41016)
  • [15] Y. Maday and B. Métivet, Chebyshev spectral approximation of Navier-Stokes equations in a two-dimensional domain, Modél. Math. Anal. Numér. 21 (1987), 93-123. MR 882688 (88j:65222)
  • [16] S. A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech. 50 (1971), 689-703.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N35, 65D30, 76D05, 76M25

Retrieve articles in all journals with MSC: 65N35, 65D30, 76D05, 76M25

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society