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Exponential convergence of adaptive quarklet approximation
Journal of Complexity ( IF 1.7 ) Pub Date : 2020-02-28 , DOI: 10.1016/j.jco.2020.101470
Stephan Dahlke , Thorsten Raasch , Alexander Sieber

This paper is concerned with approximation properties of polynomially enriched wavelet systems, so-called quarklet frames. We show that certain model singularities that arise in elliptic boundary value problems on polygonal domains can be approximated from the span of such quarklet systems at inverse-exponential rates. In order to realize these, we combine spatial refinement in the vicinity of the singularities with suitable growth of the polynomial degrees in regions where the solution is smooth, similar to adaptive hp-finite element approximation.



中文翻译:

自适应四方近似的指数收敛

本文关注的是多项式富集的小波系统的近似性质,即所谓的四重框架。我们表明,在多边形域上的椭圆边界值问题中出现的某些模型奇异性可以从此类夸克系统的跨度以反指数速率近似得出。为了实现这些,我们将奇异点附近的空间细化与多项式的适当增长相结合,在该区域中解很平滑,类似于自适应hp有限元逼近。

更新日期:2020-02-28
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