The MINI mixed finite element for the Stokes problem: An experimental investigation

Andrea Cioncolini, Daniele Boffi

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    Abstract

    푂 ℎ! ! superconvergence in pressure and velocity has been experimentally investigated for the twodimensional Stokes problem discretized with the MINI mixed finite element. Even though the classic mixed finite element theory for the MINI element guarantees linear convergence for the total error, recent theoretical results indicate that superconvergence of order 푂 ℎ! ! in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured, threedirectional triangular meshes. The numerical experiments presented here suggest a more general validity of 푂 ℎ! ! superconvergence, possibly to automatically generated and unstructured triangulations. In addition, the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise-linear part of the computed velocity, finding that the former is generally closer to the exact velocity, whereas the latter conserves mass better.
    Original languageEnglish
    JournalComputers and Mathematics with Applications
    Early online date2 Jan 2019
    DOIs
    Publication statusPublished - 2019

    Keywords

    • Stokes problem
    • Mixed finite element methods
    • MINI finite element
    • Superconvergence
    • Benchmark numerical experiments

    Research Beacons, Institutes and Platforms

    • Dalton Nuclear Institute

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