Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

We present the lifting scheme, a simple construction of second generation wavelets; these
are wavelets that are not necessarily translates and dilates of one fixed function. Such …

This is a survey of nonlinear approximation, especially that part of the subject which is
important in numerical computation. Nonlinear approximation means that the approximants …

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 …

In this paper an adaptive finite element method is constructed for solving elliptic equations
that has optimal computational complexity. Whenever, for some s> 0, the solution can be …

This is a survey on the theory of adaptive finite element methods (AFEM), which are
fundamental in modern computational science and engineering. We present a self …

This paper is concerned with the construction and analysis of wavelet-based adaptive
algorithms for the numerical solution of elliptic equations. These algorithms approximate the …

More than anything else, the increase of computing power seems to stimulate the greed for
tackling ever larger problems involving large-scale numerical simulation. As a consequence …

This survey article is concerned with two basic approximation concepts and their
interrelation with the numerical solution of elliptic operator equations, namely nonlinear and …

We study inhomogeneous boundary value problems for the Laplacian in arbitrary Lipschitz
domains with data in Sobolev–Besov spaces. As such, this is a natural continuation of work …