Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

Tractability of Multivariate Problems Volume III: Standard Information for Operators Page 1
Tracts in Mathematics 18 Erich Novak Henryk Woz , niakowski Tractability of Multivariate …

Adaptive Finite Element Methods for numerically solving elliptic equations are used often in
practice. Only recently [12],[17] have these methods been shown to converge. However, this …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value
problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet …

Regularization of ill-posed linear inverse problems via ℓ 1 penalization has been proposed
for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer …

We propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …

In this paper we propose and analyze stable variational formulations for convection diffusion
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …

In" Adaptive wavelet methods II---Beyond the elliptic case" of Cohen, Dahmen, and DeVore
[Found. Comput. Math., 2 (2002), pp. 203--245], an adaptive method has been developed for …