Optimal higher-order convergence rates for parabolic multiscale problems
Numerical Analysis
2026-05-15 v2 Numerical Analysis
Abstract
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to enrich the multiscale spaces, ensuring higher-order convergence without requiring assumptions on the coefficient beyond boundedness. This approach addresses the challenge of a reduction of convergence rates when applying higher-order LOD methods to time-dependent problems. Addressing a parabolic equation as a model problem, we prove the exponential decay of these enriched corrections and establish rigorous a priori error estimates. Numerical experiments confirm our theoretical results.
Cite
@article{arxiv.2510.09514,
title = {Optimal higher-order convergence rates for parabolic multiscale problems},
author = {Balaje Kalyanaraman and Felix Krumbiegel and Roland Maier and Siyang Wang},
journal= {arXiv preprint arXiv:2510.09514},
year = {2026}
}