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• W3127832849 abstract "Asymptotic expansions are derived for eigenvalues produced by both the Crouzeix-Raviart element and the enriched Crouzeix--Raviart element. The expansions are optimal in the sense that extrapolation eigenvalues based on them admit a fourth order convergence provided that exact eigenfunctions are smooth enough. The major challenge in establishing the expansions comes from the fact that the canonical interpolation of both nonconforming elements lacks a crucial superclose property, and the nonconformity of both elements. The main idea is to employ the relation between the lowest-order mixed Raviart--Thomas element and the two nonconforming elements, and consequently make use of the superclose property of the canonical interpolation of the lowest-order mixed Raviart--Thomas element. To overcome the difficulty caused by the nonconformity, the commuting property of the canonical interpolation operators of both nonconforming elements is further used, which turns the consistency error problem into an interpolation error problem. Then, a series of new results are obtained to show the final expansions." @default.
• W3127832849 created "2021-02-15" @default.
• W3127832849 creator A5028500115 @default.
• W3127832849 creator A5068650382 @default.
• W3127832849 date "2019-02-23" @default.
• W3127832849 modified "2023-09-25" @default.
• W3127832849 title "Asymptotic expansions of eigenvalues by both the Crouzeix-Raviart and enriched Crouzeix-Raviart elements" @default.
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• W3127832849 doi "https://doi.org/10.48550/arxiv.1902.09524" @default.
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