Volume 52, Issue 3
A New Mixed Method for the Stokes Equations Based on Stress-Velocity-Vorticity Formulation

Mattia Penati & Edie Miglio

J. Math. Study, 52 (2019), pp. 299-319.

Published online: 2019-09

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  • Abstract

In this paper, we develop and analyze a mixed finite element method for the Stokes flow. This method is based on a stress-velocity-vorticity formulation. A new discretization is proposed: the stress is approximated using the Raviart-Thomas elements, the velocity and the vorticity by piecewise discontinuous polynomials. It is shown that if the orders of these spaces are properly chosen then the advocated method is stable. We derive error estimates for the Stokes problem, showing optimal accuracy for both the velocity and vorticity.

  • Keywords

Mixed finite element, Stokes equations, Raviart-Thomas, incompressible fluids.

  • AMS Subject Headings

65N12, 65N30, 76D07, 76M10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mattia.penati@polimi.it (Mattia Penati)

edie.miglio@polimi.it (Edie Miglio)

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