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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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1)
- Efficient P1-FEM for Any Space Dimension in Matlab
- Adaptive Image Compression via Optimal Mesh Refinement
- Wave Propagation in High-Contrast Media: Periodic and Beyond
- On a Mixed FEM and a FOSLS with 𝐻−1 Loads
- A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density
- A Time Splitting Method for the Three-Dimensional Linear Pauli Equation
- Simultaneous Reconstruction of Speed of Sound and Nonlinearity Parameter in a Paraxial Model of Vibro-Acoustography in Frequency Domain
- Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems
- Nonlinear PDE Models in Semi-relativistic Quantum Physics
- Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise
- Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods
- A Posteriori Error Estimation for the Optimal Control of Time-Periodic Eddy Current Problems
Artikel in diesem Heft
- Frontmatter
- Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1)
- Efficient P1-FEM for Any Space Dimension in Matlab
- Adaptive Image Compression via Optimal Mesh Refinement
- Wave Propagation in High-Contrast Media: Periodic and Beyond
- On a Mixed FEM and a FOSLS with 𝐻−1 Loads
- A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density
- A Time Splitting Method for the Three-Dimensional Linear Pauli Equation
- Simultaneous Reconstruction of Speed of Sound and Nonlinearity Parameter in a Paraxial Model of Vibro-Acoustography in Frequency Domain
- Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems
- Nonlinear PDE Models in Semi-relativistic Quantum Physics
- Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise
- Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods
- A Posteriori Error Estimation for the Optimal Control of Time-Periodic Eddy Current Problems