@Article{ Griebel.Knapek:2000,
author = {M.~Griebel and S.~Knapek},
title = {Optimized tensor-product approximation spaces},
journal = {Constructive Approximation},
year = {2000},
optkey = {},
volume = {16},
number = {4},
pages = {525--540},
optmonth = {},
abstract = {This paper is concerned with the construction of optimized
grids and approximation spaces for elliptic differential
and integral equations. The main result is the analysis of
the approximation of the embedding of the intersection of
classes of functions with bounded mixed derivatives in
standard Sobolev spaces. Based on the framework of
tensor-product biorthogonal wavelet bases and stable
subspace splittings, the problem is reduced to diagonal
mappings between Hilbert sequence spaces. We construct
operator adapted finite-element subspaces with a lower
dimension than the standard full-grid spaces. These new
approximation spaces preserve the approximation order of
the standard full-grid spaces, provided that certain
additional regularity assumptions are fulfilled. The form
of the approximation spaces is governed by the ratios of
the smoothness exponents of the considered classes of
functions. We show in which cases the so called curse of
dimensionality can be broken. The theory covers elliptic
boundary value problems as well as boundary integral
equations.},
optnote = {},
annote = {article,245C},
ps = {http://wissrech.ins.uni-bonn.de/research/pub/knapek/finalCA.ps.gz}
}