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Mathematics > Numerical Analysis

arXiv:2006.02952 (math)
[Submitted on 4 Jun 2020]

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

Authors:Xuefeng Liu, Mitsuhiro Nakao, Chun'guang You, Shin'ichi Oishi
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Abstract: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.
Comments: 8 tables
Subjects: Numerical Analysis (math.NA)
MSC classes: 76M10, 65N30, 5N25
Cite as: arXiv:2006.02952 [math.NA]
  (or arXiv:2006.02952v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2006.02952

Submission history

From: Xuefeng Liu [view email]
[v1] Thu, 4 Jun 2020 15:35:19 UTC (34 KB)
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