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arXiv · 2510.09514

Optimal higher-order convergence rates for parabolic multiscale problems

Balaje Kalyanaraman·Felix Krumbiegel·Roland Maier·Siyang Wang
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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.

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Balaje Kalyanaraman, Felix Krumbiegel, Roland Maier, Siyang Wang. 2025-10-10. Optimal higher-order convergence rates for parabolic multiscale problems. https://arxiv.org/abs/2510.09514

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