For the Oseen problem, we present a new stabilized virtual element method on polygonal meshes that allows us to employ “equal-order” virtual element pairs to approximate both velocity and pressure. By introducing the local projection type stabilization terms to the virtual element method, the method can not only circumvent the discrete Babuška-Brezzi condition, but also maintain the favorable stability and approximation properties of residual-based stabilization methods. In particular, it does not need to calculate complex high-order derivative terms and avoids the strong coupling terms of velocity and pressure. Error estimates are obtained without depending on the inverse of the viscosity, which means that the method is effective in the convective-dominated regime. Some numerical experiments are performed to verify the method has good behaviors.

对于 Oseen 问题，我们提出了一种新的多边形网格稳定虚拟单元方法，它允许我们使用“等阶”虚拟单元对来近似速度和压力。通过在虚元法中引入局部投影型稳定项，该方法不仅可以规避离散的Babuška-Brezzi条件，而且保持了基于残差的稳定方法良好的稳定性和逼近性。特别是不需要计算复杂的高阶导数项，避免了速度和压力的强耦合项。在不依赖于粘度倒数的情况下获得误差估计，这意味着该方法在对流占主导地位的情况下是有效的。进行了一些数值实验以验证该方法具有良好的行为。