Some spectral approximations of twodimensional fourthorder problems
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 by Christine Bernardi, Giuseppe Coppoletta and Yvon Maday PDF
 Math. Comp. 59 (1992), 6376 Request permission
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

C. Bernardi, G. Coppoletta, and Y. Maday, Some spectral approximations of multidimensional fourthorder problems, Internal Report 90021, Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Paris, 1990.
 Christine Bernardi and Yvon Maday, Some spectral approximations of onedimensional fourthorder problems, Progress in approximation theory, Academic Press, Boston, MA, 1991, pp. 43–116. MR 1114769 —, Spectral methods, Handbook of Numerical Analysis (P. G. Ciarlet and J.L. Lions, eds.), NorthHolland (to appear).
 C. Bernardi and G. Raugel, Méthodes d’éléments finis mixtes pour les équations de Stokes et de NavierStokes dans un polygone non convexe, Calcolo 18 (1981), no. 3, 255–291 (French, with English summary). MR 647827, DOI 10.1007/BF02576359
 Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang, Spectral methods in fluid dynamics, Springer Series in Computational Physics, SpringerVerlag, New York, 1988. MR 917480, DOI 10.1007/9783642841088
 C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp. 38 (1982), no. 157, 67–86. MR 637287, DOI 10.1090/S00255718198206372873
 Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, 2nd ed., Computer Science and Applied Mathematics, Academic Press, Inc., Orlando, FL, 1984. MR 760629
 Daniele Funaro and Wilhelm Heinrichs, Some results about the pseudospectral approximation of onedimensional fourthorder problems, Numer. Math. 58 (1990), no. 4, 399–418. MR 1077586, DOI 10.1007/BF01385633
 Luigi Gatteschi, Su una formula di quadratura “quasi gaussiana”. Tabulazione delle ascisse d’integrazione e delle relative costanti di Christoffel, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 98 (1963/64), 641–661 (Italian). MR 166920
 P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683 E. B. Karpilovskaya, A method of collocation for integrodifferential equations with biharmonic principal part, U.S.S.R. Comput. Math. and Math. Phys. 10 (1970), no. 6, 240246. O. Koutchmy (in preparation).
 J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
 Yvon Maday, Résultats d’approximation optimaux pour les opérateurs d’interpolation polynomiale, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 9, 705–710 (French, with English summary). MR 1105630
 Y. Maday and B. Métivet, Chebyshev spectral approximation of NavierStokes equations in a twodimensional domain, RAIRO Modél. Math. Anal. Numér. 21 (1987), no. 1, 93–123 (English, with French summary). MR 882688, DOI 10.1051/m2an/1987210100931 S. A. Orszag, Accurate solution of the OrrSommerfeld stability equation, J. Fluid Mech. 50 (1971), 689703.
Additional Information
 © Copyright 1992 American Mathematical Society
 Journal: Math. Comp. 59 (1992), 6376
 MSC: Primary 65N35; Secondary 65D30, 76D05, 76M25
 DOI: https://doi.org/10.1090/S00255718199211347149
 MathSciNet review: 1134714