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The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coe±cients of some smooth functions de¯ned in a two-dimensional space. The motiva-tion of this research is to establish some fundamental mathematical
foundations needed in justifying the adaptive multiresolution anal-ysis of the hat- interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an e??ort towards this direction, we give estimates on the decaying ratios of the wavelet coe±cients at children interpolation points to the wavelet coe±cient at the parent interpolation point. We also give an estimate for the di??erence between non-adaptively and adaptively interpolated representations.
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참고문헌 (27)
참고문헌 신청
/ 1973. / Multi-level adaptive technique for fast numerical solution to boundaryvalue problems Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mechanics Lecture Notes in P
/ 1977 / Multi-level adaptive solutions to boundary value problems 31 : 333 ~ 390
/ 1978 / Error estimates for adaptive nite elementcomputations 15 : 736 ~ 754
/ 1981 / On the convergence of multigrid iterations 9 : 231 ~ 329
/ 1985 / Some a posteriori error estimators for elliptic partialdierential equations 44 : 283 ~ 301
/ 1977 / Multi-level adaptive solutions to boundary value problems 31 : 333 ~ 390
/ 1978 / Error estimates for adaptive nite elementcomputations 15 : 736 ~ 754
/ 1981 / On the convergence of multigrid iterations 9 : 231 ~ 329
/ 1985 / Some a posteriori error estimators for elliptic partialdierential equations 44 : 283 ~ 301
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