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Keywords:

  • discontinuous Galerkin;
  • incompressible Navier–Stokes;
  • strongly divergence free;
  • a posteriori error estimates;
  • adaptive mesh refinement;
  • finite element methods

Abstract

We develop the energy norm a posteriori error analysis of exactly divergence-free discontinuous RTk/Qk Galerkin methods for the incompressible Navier–Stokes equations with small data. We derive upper and local lower bounds for the velocity–pressure error measured in terms of the natural energy norm of the discretization. Numerical examples illustrate the performance of the error estimator within an adaptive refinement strategy. Copyright © 2008 John Wiley & Sons, Ltd.