Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

Xuefeng Liu*, Mitsuhiro T. Nakao, Chun’guang You, Shin’ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is solved by utilizing the extended hypercircle method along with the Scott-Vogelius finite element scheme. Since all terms in the error estimation have explicit values, by further applying the interval arithmetic and verified computing algorithms, the computed results provide rigorous estimation for the approximation error. As an application of the proposed error estimation, the eigenvalue problem of the Stokes operator is considered and rigorous bounds for the eigenvalues are obtained. The efficiency of proposed error estimation is demonstrated by solving the Stokes equation on both convex and non-convex 3D domains.

Original languageEnglish
Pages (from-to)545-559
Number of pages15
JournalJapan Journal of Industrial and Applied Mathematics
Issue number2
Publication statusPublished - 2021 Jun


  • A posteriori error estimation
  • A priori error estimation
  • Eigenvalue problem
  • Finite element method
  • Hypercircle method
  • Stokes equation

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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