Piecewise tensor product wavelet bases by extensions and approximation rates
Piecewise tensor product wavelet bases by extensions and approximation rates
复制标题
通过扩展和近似率的分段张量积小波基
DOI：
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发表时间：
2013
影响因子：
2
通讯作者：
R. Stevenson
中科院分区：
文献类型：
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作者：
N. Chegini;S. Dahlke;U. Friedrich;R. Stevenson
在这一章中，我们介绍了在DFG-SPP项目“算子方程的自适应小波框架方法：稀疏网格、向量值空间和在非线性反问题中的应用”的背景下所取得的一些主要结果。本项目主要研究非平凡区域上的(非线性)椭圆和抛物型算子方程以及相关的逆参数辨识问题。一个关键的步骤是设计一个高效的正解算器。我们采用了一种空间自适应小波Rothe格式。用基于广义张量小波的自适应小波Galerkin格式求解椭圆子问题，实现了与尺度无关的逼近速度。在这一章中，我们介绍了这些新的张量基的构造，并讨论了一些数值实验。
In this chapter, we present some of the major results that have been achieved in the context of the DFG-SPP project “Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces and Applications to Nonlinear Inverse Problems”. This project has been concerned with (nonlinear) elliptic and parabolic operator equations on nontrivial domains as well as with related inverse parameter identification problems. One crucial step has been the design of an efficient forward solver. We employed a spatially adaptive wavelet Rothe scheme. The resulting elliptic subproblems have been solved by adaptive wavelet Galerkin schemes based on generalized tensor wavelets that realize dimension-independent approximation rates. In this chapter, we present the construction of these new tensor bases and discuss some numerical experiments.