On the adaptive computation of integrals of wavelets

被引：28
作者：
Bertoluzza, S
Canuto, C
Urban, K
机构：
[1] CNR, Ist Anal Numer, I-27100 Pavia, Italy
[2] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy
[3] Rhein Westfal TH Aachen, Inst Geometrie & Prakt Math, D-52056 Aachen, Germany
来源：
APPLIED NUMERICAL MATHEMATICS | 2000年 / 34卷 / 01期
关键词：
adaptive wavelet methods; integrals; numerical methods for pde's;
D O I：
10.1016/S0168-9274(99)00028-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The numerical solution of partial differential equations involves the computation of integrals of products of given functions and (derivatives of) trial and test functions. We study this problem using adaptively chosen wavelet bases. Firstly, we reduce this problem to the computation of 1-dimensional integrals and present an algorithm for computing these integrals, Then, we consider appropriate adaptive approximations and study the induced error. Finally, we give numerical results. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
引用
收藏
页码：13 / 38
页数：26
相关论文
共 36 条
[1]  
BARINKA A, 1998, 156 IGPM RWTH AACH
[2]  
BARSCH T, 1998, 158 IGPM RWTH AACH
[3]  
BARSCH T, COMMUNICATION
[4]  
BERTOLUZZA S, 1997, MULTISCALE WAVELET M, P109
[5]   FAST WAVELET TRANSFORMS AND NUMERICAL ALGORITHMS .1. [J].
BEYLKIN, G ;
COIFMAN, R ;
ROKHLIN, V .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (02) :141-183
[6]   The Wavelet Element Method part I. Construction and analysis [J].
Canuto, C ;
Tabacco, A ;
Urban, K .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1999, 6 (01) :1-52
[7]  
CANUTO C, 1997, IN PRESS APPL COMPUT
[8]  
CANUTO C, 1996, IN PRESS ANN MAT PUR
[9]  
Cohen A., 1993, Applied and Computational Harmonic Analysis, V1, P54, DOI 10.1006/acha.1993.1005
[10]   BIORTHOGONAL BASES OF COMPACTLY SUPPORTED WAVELETS [J].
COHEN, A ;
DAUBECHIES, I ;
FEAUVEAU, JC .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (05) :485-560
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