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

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**The MINI mixed finite element for the Stokes problem : An experimental investigation.** / Boffi, Daniele; Cioncolini, Andrea.

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*Computers and Mathematics with Applications*, Vuosikerta. 77, Nro 9, Sivut 2432-2446. https://doi.org/10.1016/j.camwa.2018.12.028

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*Computers and Mathematics with Applications*,

*77*(9), 2432-2446. https://doi.org/10.1016/j.camwa.2018.12.028

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TY - JOUR

T1 - The MINI mixed finite element for the Stokes problem

T2 - An experimental investigation

AU - Boffi, Daniele

AU - Cioncolini, Andrea

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Oh 3∕2 superconvergence in pressure and velocity has been experimentally investigated for the two-dimensional 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 Oh 3∕2 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, three-directional triangular meshes. The numerical experiments presented here suggest a more general validity of Oh 3∕2 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.

AB - Oh 3∕2 superconvergence in pressure and velocity has been experimentally investigated for the two-dimensional 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 Oh 3∕2 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, three-directional triangular meshes. The numerical experiments presented here suggest a more general validity of Oh 3∕2 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.

KW - Benchmark numerical experiments

KW - MINI finite element

KW - Mixed finite element method

KW - Stokes problem

KW - Superconvergence

UR - http://www.scopus.com/inward/record.url?scp=85059308030&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.12.028

DO - 10.1016/j.camwa.2018.12.028

M3 - Article

VL - 77

SP - 2432

EP - 2446

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 9

ER -

ID: 33658620