A Note on the Construction of L-Fold Sparse Tensor Product Spaces

被引：13
作者：
Griebel, Michael [1 ]
Harbrecht, Helmut [2 ]
机构：
[1] Univ Bonn, Inst Numer Simulat, D-53115 Bonn, Germany
[2] Univ Basel, Math Inst, CH-4051 Basel, Switzerland
来源：
CONSTRUCTIVE APPROXIMATION | 2013年 / 38卷 / 02期
关键词：
High-dimensional problems; Sparse grids; Sparse tensor product spaces; Tensor product domains of different dimensions; Sparse tensor product of ansatz spaces with different approximation power; Optimal construction of sparse grids; Rate of approximation; PERIODIC UNFOLDING METHOD; FINITE-ELEMENTS; ELLIPTIC PROBLEMS; APPROXIMATION; ORDER;
D O I：
10.1007/s00365-012-9178-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper, we consider the construction of general sparse tensor product spaces in arbitrary space dimensions when the single subdomains are of different dimensionality and the associated ansatz spaces possess different approximation properties. Our theory extends the results from Griebel and Harbrecht (Math. Comput., 2013) for the construction of two-fold sparse tensor product space to arbitrary L-fold sparse tensor product spaces.
引用
收藏
页码：235 / 251
页数：17
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