Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MINIMAL LOCALLY STABILIZED Q1-Q0 SCHEMES FOR THE GENERALIZED STOKES PROBLEM

  • Chibani, Alima (Department of Mathematics Faculty of Exact Sciences University Freres Mentouri) ;
  • Kechkar, Nasserdine (Department of Mathematics Faculty of Exact Sciences University Freres Mentouri)
  • Received : 2019.09.12
  • Accepted : 2020.06.10
  • Published : 2020.09.01
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Abstract

In this paper, some novel discrete formulations for stabilizing the mixed finite element method Q1-Q0 (bilinear velocity and constant pressure approximations) are introduced and discussed for the generalized Stokes problem. These are based on stabilizing discontinuous pressure approximations via local jump operators. The developing idea consists in a reduction of terms in the local jump formulation, introduced earlier, in such a way that stability and convergence properties are preserved. The computer implementation aspects and numerical evaluation of these stabilized discrete formulations are also considered. For illustrating the numerical performance of the proposed approaches and comparing the three versions of the local jump methods alongside with the global jump setting, some obtained results for two test generalized Stokes problems are presented. Numerical tests confirm the stability and accuracy characteristics of the resulting approximations.

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References

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