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Numerical simulations of the steady Navier-Stokes equations using adaptive meshing schemes

A 2007 Preprint by L. Ju and L. Tian

  • 2007:03
  • In this paper, we consider an adaptive meshing scheme for solution of the steady incompressible Navier-Stokes equations by finite element discretizations. The mesh refinement and optimization are performed based on an algorithm that combines the so-call conforming centroidal Voronoi Delaunay triangulations and residual-type local a posteriori error estimators. Numerical experiments for various examples are presented with quadratic finite elements used for the velocity field and linear finite elements for the pressure. The results show that our meshing scheme can equally distribute the errors over all elements in a quite optimal way and keep the triangles very well shaped as well at all levels of refinement. In addition, the convergence rates achieved are close to the best obtainable.

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