Abstract
The paper presents a new proof of the \(C^0\)IPG method (\(C^0\) interior penalty Galerkin method) for the biharmonic eigenvalue problem. Instead of using the proof following the structure of discontinuous Galerkin method, we rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for \(C^0\)IPG is proved using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method which is easy in coding to compute the eigenvalues. Numerical examples are presented to validate the theory.
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Acknowledgements
The research of Y. Xi is supported in part by the National Natural Science Foundation of China with Grant No.11901295, Natural Science Foundation of Jiangsu Province under BK20190431. The research of X. Ji is partially supported by the National Natural Science Foundation of China with Grant Nos.11971468, Beijing Natural Science Foundation Z200003.
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Xi, Y., Ji, X. A New Method using \(C^0\)IPG for the Biharmonic Eigenvalue Problem. J Sci Comput 90, 81 (2022). https://doi.org/10.1007/s10915-022-01762-6
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DOI: https://doi.org/10.1007/s10915-022-01762-6