Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements

DOI10.1007/s13160-017-0291-7zbMath1450.65143OpenAlexW2783934070MaRDI QIDQ1742892

Xuefeng Liu, Hehu Xie, Manting Xie

Publication date: 12 April 2018

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-017-0291-7

zbMATH Keywords

eigenvalue boundCrouzeix-Raviart elementoptimal convergenceexplicit lower boundenriched Crouzeix-Raviart elementStokes eigenproblem

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (10)

Fully computable a posteriori error bounds for eigenfunctions ⋮ Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients. ⋮ Projection-based guaranteed \(L^2\) error bounds for finite element approximations of Laplace eigenfunctions ⋮ The discontinuous Galerkin and the nonconforming ECR element approximations for an MHD Stokes eigenvalue problem ⋮ Guaranteed lower eigenvalue bounds for two spectral problems arising in fluid mechanics ⋮ Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering ⋮ Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations ⋮ Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms ⋮ The a posteriori error estimates and adaptive computation of nonconforming mixed finite elements for the Stokes eigenvalue problem ⋮ Computable error estimates for ground state solution of Bose-Einstein condensates

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