Optimal higher-order convergence rates for parabolic multiscale problems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916012302008320 |
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| author | Kalyanaraman, Balaje Krumbiegel, Felix Maier, Roland Wang, Siyang |
| author_facet | Kalyanaraman, Balaje Krumbiegel, Felix Maier, Roland Wang, Siyang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal higher-order convergence rates for parabolic multiscale problems Kalyanaraman, Balaje Krumbiegel, Felix Maier, Roland Wang, Siyang Numerical Analysis 65M12, 65M15, 65M60, 35K20 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. |
| title | Optimal higher-order convergence rates for parabolic multiscale problems |
| topic | Numerical Analysis 65M12, 65M15, 65M60, 35K20 |
| url | https://arxiv.org/abs/2510.09514 |