In this article, we consider a local projection stabilisation for a Hybrid High-Order (HHO) approximation of the Oseen problem. We prove an existence-uniqueness result under a stronger SUPG-like norm. We improve the stability and provide error estimation in stronger norm for convection dominated Oseen problem. We also derive an optimal order error estimate under the SUPG-like norm for equal-order polynomial discretisation of velocity and pressure spaces. Numerical experiments are performed to validate the theoretical results.

翻译：本文研究Oseen问题的混合高阶（HHO）近似中的局部投影稳定化方法。我们在更强的类SUPG范数下证明了解的存在唯一性。针对对流主导的Oseen问题，我们提升了稳定性并在更强范数下给出误差估计。对于速度和压力空间的等阶多项式离散，我们还推导了类SUPG范数下的最优阶误差估计。数值实验验证了理论结果。