# Boundary conditions for the Stokes problem and a pressure-Poisson problem

## TL;DR

This paper introduces a new boundary condition formulation for the pressure-Poisson problem related to the stationary Stokes equations, providing error estimates and connecting boundary conditions to solution accuracy.

## Contribution

It proposes an innovative boundary condition for the pressure-Poisson problem and establishes error estimates linking it to the Stokes problem solutions.

## Key findings

- New boundary condition formulation for pressure-Poisson problem
- Error estimates between Stokes and pressure-Poisson solutions
- Connection of boundary conditions to solution accuracy

## Abstract

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).