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

Daniele Boffi, Andrea Cioncolini*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2432-2446
Number of pages15
JournalComputers and Mathematics with Applications
Volume77
Issue number9
DOIs
Publication statusPublished - 1 May 2019
MoE publication typeA1 Journal article-refereed

Keywords

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

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