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Spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in circular domain
Author(s) -
Tan Ting,
An Jing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4863
Subject(s) - mathematics , eigenvalues and eigenvectors , sobolev space , galerkin method , domain (mathematical analysis) , transformation (genetics) , mathematical analysis , sequence (biology) , finite element method , physics , quantum mechanics , thermodynamics , biochemistry , chemistry , genetics , biology , gene
In this paper, we present spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in a circular domain. First of all, we use the polar coordinate transformation and technique of separation of variables to reduce the problem to a sequence of equivalent 1‐dimensional eigenvalue problems that can be solved individually in parallel. Then, we derive the pole conditions and introduce weighted Sobolev space according to pole conditions. Together with the approximate properties of orthogonal polynomials, we prove the error estimates of approximate eigenvalues for each 1‐dimensional eigenvalue problem. Finally, we provide some numerical experiments to validate the theoretical results and algorithms.