Journal
AIMS MATHEMATICS
Volume 7, Issue 5, Pages 7528-7551Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2022423
Keywords
Steklov eigenvalue problem; spectral-Galerkin method; error estimations; tensor product; numerical experiments
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Funding
- National Natural Science Foundation of China [11961009]
- Guizhou Provincial Graduate Education Innovation Program [YJSCXJH [2020] 097]
- Scientific Research Foundation of Guizhou University of Finance and Economics [2020XYB10]
- Project for Young Talents Growth of Guizhou Provincial Department of Education [KY[2022]179]
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An efficient spectral method is proposed for a new Steklov eigenvalue problem in inverse scattering. The weak form and the associated discrete scheme are established by introducing an appropriate Sobolev space and a corresponding approximation space. The error estimates of approximated eigenvalues and eigenfunctions are proved using the spectral approximation results and the approximation properties of orthogonal projection operators. The algorithm is extended to the circular domain and validated through numerical experiments.
An efficient spectral method is proposed for a new Steklov eigenvalue problem in inverse scattering. Firstly, we establish the weak form and the associated discrete scheme by introducing an appropriate Sobolev space and a corresponding approximation space. Then, according to the Fredholm Alternative, the corresponding operator forms of weak formulation and discrete formulation are derived. After that, the error estimates of approximated eigenvalues and eigenfunctions are proved by using the spectral approximation results of completely continuous operators and the approximation properties of orthogonal projection operators. We also construct an appropriate set of basis functions in the approximation space and derive the matrix form of the discrete scheme based on the tensor product. In addition, we extend the algorithm to the circular domain. Finally, we present plenty of numerical experiments and compare them with some existing numerical methods, which validate that our algorithm is effective and high accuracy.
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