Anisotropic approximation on space–time domains

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2026-08-01 Epub Date: 2026-01-08 DOI:10.1016/j.jat.2025.106282

Pedro Morin , Cornelia Schneider , Nick Schneider

引用次数: 0

Abstract

We investigate anisotropic (piecewise) polynomial approximation of functions in Lebesgue spaces as well as anisotropic Besov spaces. For this purpose we study temporal and spatial moduli of smoothness and their properties. In particular, we prove Jackson- and Whitney-type inequalities on Lipschitz cylinders, i.e., space–time domains

I \times D

with a finite interval

I

and a bounded Lipschitz domain

D \subset R^{d}

d \in N

. As an application, we prove a direct estimate result for adaptive space–time finite element approximation in the discontinuous setting.

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时空域的各向异性近似

研究了Lebesgue空间和Besov空间中函数的各向异性（分段）多项式逼近。为此，我们研究了平滑度的时间模量和空间模量及其性质。特别地，我们证明了Lipschitz柱面上的Jackson-型不等式和whitney -型不等式，即具有有限区间I和有界Lipschitz域D∧Rd， D∈N的时空域I×D。作为应用，证明了不连续环境下自适应时空有限元逼近的一个直接估计结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.