Analysis and Approximation of a Vorticity–Velocity–Pressure Formulation for the Oseen Equations

V. Anaya, A. Bouharguane, D. Mora, C. Reales, R. Ruiz-Baier, N. Seloula, H. Torres

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Abstract

We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous problem is addressed by invoking a global inf-sup property in an adequate abstract setting for non-symmetric systems. The proposed finite element schemes, which produce exactly divergence-free discrete velocities, are shown to be well-defined and optimal convergence rates are derived in suitable norms. This mixed finite element method is also pressure-robust. In addition, we establish optimal rates of convergence for a class of discontinuous Galerkin schemes, which employ stabilisation. A set of numerical examples serves to illustrate salient features of these methods.

Original languageEnglish
Pages (from-to)1577-1606
Number of pages30
JournalJournal of Scientific Computing
Volume80
Issue number3
DOIs
Publication statusPublished - 15 Sep 2019
Externally publishedYes

Keywords

  • A priori error bounds
  • Discontinuous Galerkin schemes
  • Exactly divergence-free velocity
  • Mixed finite elements
  • Numerical fluxes
  • Oseen equations
  • Vorticity-based formulation

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