Strong convergence estimates for pseudospectral methods
Heinrichs, Wilhelm
Applications of Mathematics, Tome 37 (1992), p. 401-417 / Harvested from Czech Digital Mathematics Library

Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.

Publié le : 1992-01-01
Classification:  34B05,  35J25,  65L10,  65L60,  65N30,  65N35
@article{104520,
     author = {Wilhelm Heinrichs},
     title = {Strong convergence estimates for pseudospectral methods},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {401-417},
     zbl = {0767.65064},
     mrnumber = {1185797},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104520}
}
Heinrichs, Wilhelm. Strong convergence estimates for pseudospectral methods. Applications of Mathematics, Tome 37 (1992) pp. 401-417. http://gdmltest.u-ga.fr/item/104520/

L. Brutman On the Lebesgue function for polynomial interpolation, Siam J. Numer. Anal. 15 (1978), 694-704. (1978) | Article | MR 0510554 | Zbl 0391.41002

C. Canuto A. Quarteroni Approximation result for orthogonal polynomials in Sobolev spaces, Math. Comput. 38 (1982), 67-86. (1982) | Article | MR 0637287

C. Canute Boundary conditions in Chebyshev and Legendre methods, Siam J. Numer. Anal. 23 (1986), 815-831. (1986) | Article | MR 0849284

C. Canuto A. Quarteroni Variational methods in the theoretical analysis of spectral approximations, in Spectral Methods for Partial Differential Equations , Society for Industrial and Applied Mathematics, Philadelphia, PA (1984), 55-78 (R. G. Voigt, D. Gottlieb and M. Y. Hussaini, eds.). (1984) | MR 0758262

C. Canuto A. Quarteroni Spectral and pseudospectral methods for parabolic problems with nonperiodic boundary conditions, Calcolo 18 (1981), 197-218. (1981) | Article | MR 0647825

C. Canuto D. Funaro The Schwarz algorithm for spectral methods, Siam J. Numer. Anal. 25 (1988), 24-40. (1988) | Article | MR 0923923

L. Collatz Differentialgleichungen, Teubner Studienbucher, Stuttgart, 1973. (1973) | MR 0352575 | Zbl 0267.65001

J. W. Cooley A. W. Lewis P. D. Walch The Fast Transform Algorithm: Programming considerations in the calculation of sine, cosine and Laplace transform, J. Sound vib. 12 (1970), 105-112. (1970)

R. De Vore On Jackson's theorem, J. Approx. Theory 1 (1968), 314-318. (1968) | Article

H. Ehlich K. Zeller Auswertung der Normen von Interpolations-operatoren, Math. Analen 164 (1986), 105-112. (1986) | MR 0194799

L. W. Kantorowitsch G. P. Akilow Funktionalanalysis in normierten Räumen, Akademie-Verlag, Berlin, 1964. (1964) | MR 0177273

I. P. Natanson Constructive function theory. III. Interpolation and approximation quadratures, Frederick Ungar Publishing CO., New York, 1965. (1965)

M. J. Pоwel On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria, Com. J. 9 (1967), 404-407. (1967) | MR 0208807

T. J. Rivlin The Lebesgue constants for polynomial interpolation, in Functional analysis and its application (H. G. Garnir et al., Springer-Verlag, ed.), Berlin-Heidelberg-New York, 1974, pp. 422-437. (1974) | MR 0399706 | Zbl 0299.41005

G. Rodrigue P. Saylor Inner/outer iterative methods and numerical Schwarz algorithm II, -Proceedings of the IBM Conference on Vector and Parallel Processors for Scientific Computations, Rome, 1985. (1985) | MR 0825967

G. Rodrigue J. Simon A generalization of the numerical Schwarz algorithm, , Computing Methods in Applied Sciences and Engineering VI (R. Glowinski and J. L. Lions, eds.), North Holland, 1984. (1984) | MR 0806784

H. A. Schwarz Gesammelte Mathematische Abhandlungen, Vol. 2, Springer-Verlag, Berlin.

G. Szegö Orthogonal polynomials, Am. Math. Soc., New York, 1939. (1939)

C. Temperton On the FACR(1) algorithm for the discrete Poisson equation, J. Соmр. Phys. 34 (1980), 314-329. (1980) | MR 0562366

G. M. Vainikko Differential Equations 1, (1965), 186-194. (1965)

G. M. Vainikko The convergence of the collocation method for nonlinear differential equations, USSR Соmр. Math. and Math. Phys. 6 (1966), 47-58. (1966) | MR 0196945

H. Werner R. Schaback Praktische Mathematik II, Springer-Verlag, Berlin-Heidelberg- New York, 1972. (1972) | MR 0520918

K. Witsch Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren, insbesondere Randwertaufgaben, Doctoral Thesis, Köln, 1974. (1974)

K. Witsch Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren, Numer. Math. 27 (1977), 339-354. (1977) | MR 0443361 | Zbl 0336.65031

T. A. Zang Y. S. Wong M. Y. Hussaini Spectral multigrid methods for elliptic equations I, J. Соmр. Phys. 48 (1992), 485-501. (1992) | MR 0755459

T. A. Zang Y. S. Wong M. Y. Hussaini Spectral multigrid methods for elliptic equations II, J. Соmр. Phys. 54 (1984), 489-507. (1984) | MR 0755456