A New Mixed Method for the Stokes Equations Based on Stress-Velocity-Vorticity Formulation

Authors

  • Mattia Penati MOX–Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
  • Edie Miglio MOX–Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

DOI:

https://doi.org/10.4208/jms.v52n3.19.05

Keywords:

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

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.

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Published

2019-09-16

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Issue

Vol. 52 No. 3 (2019)

Section

Articles

How to Cite

A New Mixed Method for the Stokes Equations Based on Stress-Velocity-Vorticity Formulation. (2019). Journal of Mathematical Study, 52(3), 299-319. https://doi.org/10.4208/jms.v52n3.19.05