Abstract
We propose an efficient algorithm based on the Legendre–Galerkin approximations for the direct solution of the biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn–Hilliard type. The key point to the efficiency of our algorithm is to construct appropriate basis functions which satisfying the corresponding boundary condition automatically and leading to linear systems with sparse matrices for the discrete variational formulations. In addition, the error estimate was driven by the minimax principle. Finally, the numerical results demonstrate the accuracy and the efficiency of this method.
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Acknowledgments
LZC would like to acknowledge the support from National Science Foundation of China (NSFC) through Grant 11301438 and 11671166, Postdoctoral Science Foundation of China through Grant 2015M580038 and President Foundation of Chinese Academy of Engineering Physics through Grant 201501043 and NSFC under Grant U1530401. QQZ would like to acknowledge the support from National Natural Science Foundation of China under Grant No. 11501224 and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University under Grant No. ZQN-PY201.
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Chen, L., An, J. & Zhuang, Q. Direct Solvers for the Biharmonic Eigenvalue Problems Using Legendre Polynomials. J Sci Comput 70, 1030–1041 (2017). https://doi.org/10.1007/s10915-016-0277-7
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DOI: https://doi.org/10.1007/s10915-016-0277-7