×

zbMATH — the first resource for mathematics

Wavelet interpolation and approximate solutions of elliptic partial differential equations. (English) Zbl 0811.65096
Tanner, Elizabeth A. (ed.) et al., Noncompact Lie groups and some of their applications: Proceedings of the NATO advanced research workshop on noncompact Lie groups and their physical applications, held in San Antonio, Texas, January 4-8, 1993. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 429, 349-366 (1994).
Summary: The paper formulates and proves a second-order interpolation result for square-integrable functions by means of locally finite series of Daubechies’ wavelets. Sample values of a sufficiently smooth function can be used as coefficients of a wavelet expansion at a fine scale, and the corresponding wavelet interpolation function converges in Sobolev norms of first order to the original function. This has applications to wavelet-Galerkin numerical solutions of elliptic partial differential equations.
For the entire collection see [Zbl 0792.00003].

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
PDF BibTeX XML Cite