Convergence estimates for the wavelet galerkin method

SIAM Journal on Numerical Analysis

Volumn 33, Issue 1, 1996, Pages 149-161

  Gomes, Sônia M ^a   Cortina, Elsa ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b Dir Gen de Invest y Desarrollo   (Argentina)

Author keywords

Convergence estimates; Galerkin method; Wavelets

Indexed keywords

EID: 0000859758     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733009     Document Type: Article

References (14)

1. E. BACRY, S. MALLAT, AND G. PAPANICOLAU, A wavelet based space-time adaptive numerical method for partial differential equations, Math. Mod. Numer. Anal., 26 (1992), pp. 793-834.
2. I. DAUBECHIES, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41 (1988), pp. 909-996.
3. G. FIX AND G. STRANG, Fourier analysis of the finite element method in Ritz-Galerkin theory, Stud. Appl. Math., 48 (1969), pp. 265-273.
4. R. GLOWINSKI, W. LAWTON, M. RAVACHOL, AND E. TENEMBAUM, Wavelet solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension, Report AD890527.1, AWARE, Inc., Cambridge, MA, 1989.
5. J. LIANDRAT AND PH. TCHAMITCHIAN, Resolution of the ID regularized Burgers equation using spatial wavelet approximation, Report 90-83, NASA-ICASE, 1990.
6. Y. MADAY, V. PERRIER, AND C. RAVEL, Adaptativité dynamique sur bases d'ondelettes pour l'approximation d'équations aux dérivées partielles, C. R. Acad. Sci. Paris, 312 I (1991), pp. 405-410.
7. 2(R), Trans. Amer. Math. Soc., 315 (1991), pp. 344-351.
8. Y. MEYER, Ondelettes et Operateurs, Hermann, Paris, 1990.
9. I. J. SCHOENBERG, Cardinal interpolation and spline functions, J. Approx. Theory, 2 (1969), pp. 167-206.
10. _, Cardinal interpolation and spline functions II: Interpolation of data of power growth, J. Approx. Theory, 6 (1972), pp. 404-420.
11. G. STRANG, Wavelets and dilation equations: A brief introduction, SIAM Rev., 31 (1989), pp. 614-627.
12. G. STRANG AND G. FIX, A Fourier analysis of the finite element method, in Constructive Aspects of Functional Analysis, Edizioni Cremonese, Rome, 1973.
13. V. THOMÉE, Spline approximation and difference schemes for the heat equation, in The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations, A. K. Aziz, ed., Academic Press, New York, 1972, pp. 711-746.
14. _, Convergence estimates for semi-discrete Galerkin methods for initial value-problems, Lecture Notes in Math., 333 (1973), pp. 243-262.