SHARP CONSISTENCY ESTIMATES FOR A PRESSURE-POISSON PROBLEM WITH STOKES BOUNDARY VALUE PROBLEMS

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).

Automated summary

A boundary value problem for the stationary Stokes problem and the corresponding pressure-Poisson equation is considered, with a new formulation proposed for the pressure-Poisson problem. Error estimates between solutions to the Stokes problem and the pressure-Poisson problem are established in terms of an additional boundary condition. Traction and pressure boundary conditions introduced by C. Conca et al (1994) are used for the Stokes problem.