Localized Orthogonal Decomposition Method with $H^1$ Interpolation for Multiscale Elliptic Problem

TL;DR

This paper introduces a localized orthogonal decomposition method with H^1 interpolation for multiscale elliptic problems, achieving accurate solutions without requiring scale separation assumptions, supported by theoretical error estimates and numerical validation.

Contribution

The paper presents a novel LOD method with H^1 interpolation that does not rely on scale separation, along with rigorous error analysis and numerical experiments.

Findings

The method provides accurate solutions without scale separation assumptions.

Theoretical a priori error estimates are established.

Numerical experiments confirm the effectiveness of the approach.

Abstract

This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for the proposed method. The theoretical results are conformed by various numerical experiments.