Enriched higher-order LOD for the wave equation achieves optimal high-order convergence rates, overcoming prior second-order saturation, with a priori estimates and numerical verification.
Optimal higher-order convergence rates for parabolic multiscale problems
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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.
fields
math.NA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A stabilized LOD multiscale method combined with novel post-processing achieves higher-order convergence rates for nondivergence-form elliptic equations under a generalized Cordes condition.
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Enriched higher-order multiscale approaches with applications to wave propagation
Enriched higher-order LOD for the wave equation achieves optimal high-order convergence rates, overcoming prior second-order saturation, with a priori estimates and numerical verification.
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A post-processed higher-order multiscale method for nondivergence-form elliptic equations
A stabilized LOD multiscale method combined with novel post-processing achieves higher-order convergence rates for nondivergence-form elliptic equations under a generalized Cordes condition.