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Heterogeneous Multiscale Method for elliptic problem without scale separation

Tao Yu, Xingye Yue, Changjuan Zhang

Abstract

This paper shows that the Heterogeneous Multiscale Method can be applied to elliptic problem without scale separation. The Localized Orthogonal Method is a special case of the Heterogeneous Multiscale Method.

Heterogeneous Multiscale Method for elliptic problem without scale separation

Abstract

This paper shows that the Heterogeneous Multiscale Method can be applied to elliptic problem without scale separation. The Localized Orthogonal Method is a special case of the Heterogeneous Multiscale Method.

Paper Structure

This paper contains 4 sections, 6 theorems, 52 equations.

Table of Contents

  1. Introduction
  2. Heterogeneous Multiscale Method
  3. Localization
  4. Acknowledgement

Key Result

Lemma 2.1

Let $u\in V$ be the solution of (R), i.e., then $P_0u=v_h$ and

Theorems & Definitions (11)

  • Lemma 2.1
  • Proof 1
  • Lemma 2.2
  • Proof 2
  • Lemma 2.3
  • Proof 3
  • Theorem 2.4
  • Proof 4
  • Remark 2.5
  • Lemma 3.1
  • ...and 1 more