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research-article

Arnold--Winther Mixed Finite Elements for Stokes Eigenvalue Problems

Authors:

Joscha Gedicke,

Arbaz KhanAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 40, Issue 5

Pages A3449 - A3469

https://doi.org/10.1137/17M1162032

Published: 01 January 2018 Publication History

Abstract

This paper is devoted to studying the Arnold--Winther mixed finite element method for two-dimensional Stokes eigenvalue problems using the stress-velocity formulation. A priori error estimates for the eigenvalue and eigenfunction errors are presented. To improve the approximation for both eigenvalues and eigenfunctions, we propose a local postprocessing. With the help of the local postprocessing, we derive a reliable a posteriori error estimator which is shown to be empirically efficient. We confirm numerically the proven higher order convergence of the postprocessed eigenvalues for convex domains with smooth eigenfunctions. On adaptively refined meshes we obtain numerically optimal higher orders of convergence of the postprocessed eigenvalues even on nonconvex domains.

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Cited By

Lepe FRivera GVellojin J(2023)Error estimates for a vorticity-based velocity–stress formulation of the Stokes eigenvalue problemJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114798420:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.cam.2022.114798
Lederer P(2023)Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problemsBIT10.1007/s10543-023-00976-w63:2Online publication date: 22-May-2023
https://dl.acm.org/doi/10.1007/s10543-023-00976-w
Lepe F(2023)Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problemAdvances in Computational Mathematics10.1007/s10444-023-10062-y49:4Online publication date: 27-Jul-2023
https://dl.acm.org/doi/10.1007/s10444-023-10062-y

Index Terms

Arnold--Winther Mixed Finite Elements for Stokes Eigenvalue Problems
1. Applied computing
  1. Physical sciences and engineering
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
      2. Partial differential equations
    2. Numerical analysis
      1. Computations in finite fields
      2. Numerical differentiation

Index terms have been assigned to the content through auto-classification.

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Published In

cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 40, Issue 5

2018

1103 pages

ISSN:1064-8275

DOI:10.1137/sjoce3.40.5

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© 2018, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2018

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Cited By

Lepe FRivera GVellojin J(2023)Error estimates for a vorticity-based velocity–stress formulation of the Stokes eigenvalue problemJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114798420:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.cam.2022.114798
Lederer P(2023)Asymptotically exact a posteriori error estimates for the BDM finite element approximation of mixed Laplace eigenvalue problemsBIT10.1007/s10543-023-00976-w63:2Online publication date: 22-May-2023
https://dl.acm.org/doi/10.1007/s10543-023-00976-w
Lepe F(2023)Interior penalty discontinuous Galerkin methods for the velocity-pressure formulation of the Stokes spectral problemAdvances in Computational Mathematics10.1007/s10444-023-10062-y49:4Online publication date: 27-Jul-2023
https://dl.acm.org/doi/10.1007/s10444-023-10062-y

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