A posteriori error estimates applied to flow in a channel with corners

The paper consists of three parts. In the first part, we investigate a posteriori error estimates for the Stokes and Navier–Stokes equations on two-dimensional polygonal domains. Special attention is paid to the sources of the constants in the estimates, as these play a crucial role in practical applications to adaptive refinements, as we also show. In the second part, we deal with the problem of determining accurately the constants that appear in the estimates. We present a technique for calculating the constant with high accuracy. In the third part, we apply the a posteriori error estimates with the constants found numerically to the technique of adaptive mesh refinement—we solve an incompressible flow problem in a domain with corners that cause singularities in the solution.