A posteriori error estimates for the stationary Navier Stokes equations with Dirac measures

TL;DR

This paper develops and analyzes an a posteriori error estimator for finite element solutions of the stationary Navier-Stokes equations with singular sources in two-dimensional polygonal domains, demonstrating reliability and efficiency through numerical tests.

Contribution

It introduces a new a posteriori error estimator tailored for Navier-Stokes equations with Dirac measures, including theoretical analysis and numerical validation.

Findings

The estimator is reliable and locally efficient under smallness assumptions.

Numerical examples confirm the theoretical properties of the estimator.

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.