On the construction of sparse tensor product spaces

Abstract

Let Ω 1 ⊂ R n1 and Ω 2 ⊂ R n2 be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness r 1 and r 2 , respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive the resulting cost complexities to approximate functions with anisotropic and isotropic smoothness on the tensor product domain Ω 1 ×Ω 2 . Numerical results validate our theoretical findings. © 2012 American Mathematical Society.