We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable ${\mathbf{W}}^{1,p}\times {\mathrm{L}}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element discretizations. We prove, in two and three dimensional Lipschitz, but not necessarily convex polytopal domains, that the devised error estimators are reliable and locally efficient. On the basis of the devised error estimators, we design a simple adaptive strategy that yields optimal experimental rates of convergence for the numerical examples that we perform.

中文翻译：

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具有Dirac测度的Stokes系统在W ^1，p  ×L ^p空间中的后验误差估计

我们采用合适的奇异源设计和分析Stokes系统的后验误差估计量 ${\mathbf{w\; ^}}^{\mathrm{1个}，p}\times {\mathrm{大号}}^p$空格。我们认为经典的低阶infsup稳定和稳定的有限元离散化。我们在二维和三维Lipschitz（但不一定是凸多边域）中证明，设计的误差估计器是可靠的且局部有效的。基于设计的误差估计器，我们设计了一种简单的自适应策略，可以为我们执行的数值示例产生最佳的实验收敛速度。