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Convergence analysis of an efficient spectral element method for Stokes eigenvalue problem
Author(s) -
Zhang Jun,
Wang JinRong,
Zhou Yong
Publication year - 2020
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.6388
Subject(s) - mathematics , eigenvalues and eigenvectors , legendre polynomials , convergence (economics) , norm (philosophy) , mathematical analysis , minimax , spectral element method , degree of a polynomial , polynomial , spectral method , numerical analysis , grid , finite element method , mathematical optimization , mixed finite element method , geometry , physics , quantum mechanics , political science , law , economics , thermodynamics , economic growth
In this work, an efficient Legendre spectral element method was proposed to solve the two‐dimensional Stokes eigenvalue problem on L‐shaped domain. Based on minimax principle, the rigorous error estimates of the approximate eigenvalues are proved. The approximate eigenvalues converge with the order O ( h 2 min ( N − 1 , s − 2 )N 2 ( 2 − s ) ) in L 2 norm, where h , N , and s are space grid size, polynomial degree, and the regularity of exact solution, respectively. Several numerical examples are provided to verify the theoretical analysis and demonstrate the effectiveness of the proposed scheme.