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Numerische Mathematik

, Volume 133, Issue 1, pp 37–66 | Cite as

A natural nonconforming FEM for the Bingham flow problem is quasi-optimal

  • C. Carstensen
  • B. D. Reddy
  • M. Schedensack
Article
  • 281 Downloads

Abstract

This paper introduces a novel three-field formulation for the Bingham flow problem and its two-dimensional version named after Mosolov together with low-order discretizations: a nonconforming for the classical formulation and a mixed finite element method for the three-field model. The two discretizations are equivalent and quasi-optimal in the sense that the \(H^1\) error of the primal variable is bounded by the error of the \(L^2\) best-approximation of the stress variable. This improves the predicted convergence rate by a log factor of the maximal mesh-size in comparison to the first-order conforming finite element method in a model scenario. Despite that numerical experiments lead to comparable results, the nonconforming scheme is proven to be quasi-optimal while this is not guaranteed for the conforming one.

Mathematics Subject Classification

65N30 76M10 

Notes

Acknowledgments

The third named author was supported by the Berlin Mathematical School.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Computational Science and EngineeringYonsei UniversitySeoulKorea
  3. 3.Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa
  4. 4.Institut für Numerische SimulationUniversität BonnBonnGermany

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