Convergence rates, Part II

Zhongwei Shen

doi:10.1007/978-3-319-91214-1_7

Convergence rates, Part II

Zhongwei Shen

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In Chapter 3 we establish the O(√ε) error estimates for some two-scale expansions in H¹ and the O(ε) convergence rate for solutions u_ε in L². The results are obtained without any smoothness assumption on the coefficient matrix A. In this chapter we return to the problem of convergence rates and prove various results under some additional smoothness assumptions, using uniform regularity estimates obtained in Chapters 4–6. We shall be mainly interested in the sharp O(ε) or near sharp rates of convergence.

Original language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Pages	169-203
Number of pages	35
DOIs	https://doi.org/10.1007/978-3-319-91214-1_7
State	Published - 2018

Publication series

Name	Operator Theory: Advances and Applications
Volume	269
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

ASJC Scopus subject areas

Analysis

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10.1007/978-3-319-91214-1_7

Cite this

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abstract = "In Chapter 3 we establish the O(√ε) error estimates for some two-scale expansions in H1 and the O(ε) convergence rate for solutions uε in L2. The results are obtained without any smoothness assumption on the coefficient matrix A. In this chapter we return to the problem of convergence rates and prove various results under some additional smoothness assumptions, using uniform regularity estimates obtained in Chapters 4–6. We shall be mainly interested in the sharp O(ε) or near sharp rates of convergence.",

author = "Zhongwei Shen",

year = "2018",

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Convergence rates, Part II

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