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 …

Adaptive Finite Element Methods (AFEM) are numerical procedures that approximate the
solution to a partial differential equation (PDE) by piecewise polynomials on adaptively …

The Bramble--Hilbert lemma is a fundamental result on multivariate polynomial
approximation. It is frequently applied in the analysis of finite elements methods (FEM) used …

Geometric wavelet is a recent development in the field of multivariate nonlinear piecewise
polynomials approximation. The present study improves the geometric wavelet (GW) image …

Abstract Weighted Triebel–Lizorkin and Besov spaces on the unit ball B d in ℝ d with
weights w μ (x)=(1−| x| 2) μ− 1/2, μ≥ 0, are introduced and explored. A decomposition …

We prove the following Whitney estimate. Given 0< p ≤ ∞, r ∈ N, and d ≥ 1, there exists a
constant C (d, r, p), depending only on the three parameters, such that for every bounded …

The binary space partition (BSP) technique is a simple and efficient method to adaptively
partition an initial given domain to match the geometry of a given input function. As such, the …

This paper describes a new and efficient method for low bit-rate image coding which is
based on recent development in the theory of multivariate nonlinear piecewise polynomial …

The Easy Path Wavelet Transform (EPWT), 20 has recently been proposed by one of the
authors as a tool for sparse representations of bivariate functions from discrete data, in …

We introduce graph wedgelets-a tool for data compression on graphs based on the
representation of signals by piecewise constant functions on adaptively generated binary …