We analyze, on two dimensional polygonal domains, classical low–order inf-sup stable finite element approximations of the stationary Navier–Stokes equations with singular sources. We operate under the assumptions that the continuous and discrete solutions are sufficiently small. We perform an a priori error analysis on convex domains. On Lipschitz, but not necessarily convex, polygonal domains, we design an a posteriori error estimator and prove its global reliability. We also explore efficiency estimates. We illustrate the theory with numerical tests.

中文翻译：

---

带有Dirac测度的Navier-Stokes方程的FEM离散化的误差估计

我们在二维多边形域上分析带有奇异源的平稳Navier-Stokes方程的经典低阶inf-up稳定有限元逼近。我们假设连续和离散解足够小。我们对凸域执行先验误差分析。在Lipschitz（但不一定是凸多边形）区域上，我们设计了后验误差估计器，并证明了其全局可靠性。我们还探讨了效率估算。我们通过数值测试来说明该理论。