We consider a boundary value problem for the stationary Stokes problem and the corresponding pressure-Poisson equation. We propose a new formulation for the pressure-Poisson problem with an appropriate additional boundary condition. We establish error estimates between solutions to the Stokes problem and the pressure-Poisson problem in terms of the additional boundary condition. As boundary conditions for the Stokes problem, we use a traction boundary condition and a pressure boundary condition introduced in C. Conca et al (1994).

中文翻译：

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具有Stokes边值问题的压力-泊松问题的清晰一致性估计

我们考虑固定斯托克斯问题的边值问题和相应的压力泊松方程。我们为压力-泊松问题提出了一种新的公式，并附加了适当的边界条件。根据附加的边界条件，我们在斯托克斯问题和压力泊松问题的解决方案之间建立了误差估计。作为斯托克斯问题的边界条件，我们使用C.Conca等人（1994）引入的牵引边界条件和压力边界条件。