Abstract
For the eigenvalue problem of the Steklov differential operator, an algorithm based on the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed lower eigenvalue bounds utilize the a priori error estimation for FEM solutions to non-homogeneous Neumann boundary value problems, which is obtained by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples demonstrate the efficiency of our proposed method.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11426039
Award Identifier / Grant number: 12061057
Award Identifier / Grant number: 11571023
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 20H01820
Award Identifier / Grant number: 21H00998
Funding statement: The first author is supported by JST SPRING, Grant Number JPMJSP2121. The second author has been supported by the National Natural Science Foundation of China (Nos. 11426039, 12061057, 11571023). The last author is supported by Japan Society for the Promotion of Science: Fund for the Promotion of Joint International Research (Fostering Joint International Research (A)) 20KK0306, Grant-in-Aid for Scientific Research (B) 20H01820, 21H00998. This work also received support from the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
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