Adaptive methods for PDE's: wavelets or mesh refinement?
数值分析
2025-10-20 v1 数值分析
摘要
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for the use of such bases in this context is their good performances in data compression and the approximation theoretic foundations which allow to analyze and optimize these performances. We shall discuss these theoretical foundations, as well as one of the approaches which has been followed in developing efficient adaptive wavelet solvers. We shall also discuss the similarities and differences between wavelet methods and adaptive mesh refinement.
引用
@article{arxiv.math/0212414,
title = {Adaptive methods for PDE's: wavelets or mesh refinement?},
author = {Albert Cohen},
journal= {arXiv preprint arXiv:math/0212414},
year = {2025}
}