Title: A Posteriori Error Estimates for the Stationary Navier--Stokes Equations with Dirac Measures
Abstract: In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier--Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a smallness assumption on the continuous and discrete solutions, we prove that the devised error estimator is reliable and locally efficient. We illustrate the theory with numerical examples.