We propose and analyze a high order unfitted hybridizable discontinuous Galerkin method to numerically solve Oseen equations in a domain $\Omega$ having a curved boundary. The domain is approximated by a polyhedral computational domain not necessarily fitting $\Omega$. The boundary condition is transferred to the computational domain through line integrals over the approximation of the gradient of the velocity and a suitable decomposition of the pressure in the computational domain is employed to obtain an approximation of the pressure having zero-mean in the domain $\Omega$. Under assumptions related to the distance between the computational boundary and $\Omega$, we provide stability estimates of the solution that will lead us to the well-posedness of the scheme and also to the error estimates. In particular, we prove that the approximations of the pressure, velocity and its gradient are of order $h^{k+1}$, where $h$ is the meshsize and $k$ the polynomial degree of the local discrete spaces. We provide numerical experiments validating the theory and also showing the performance of the method when applied to the steady-state incompressible Navier–Stokes equations.

我们提出并分析了一种高阶未拟合的可混合不连续伽辽金方法来数值求解域中的 Oseen 方程 $\Omega$有一个弯曲的边界。该域由多面体计算域近似，不一定适合$\Omega$. 边界条件通过速度梯度近似上的线积分转移到计算域，并在计算域中采用适当的压力分解来获得该域中具有零均值的压力的近似值$\Omega$. 在与计算边界和计算边界之间的距离相关的假设下$\Omega$，我们提供解的稳定性估计，这将使我们得到方案的适定性以及误差估计。特别地，我们证明了压力、速度及其梯度的近似值是有序的$H^{克+1}$， 在哪里 $H$ 是网格大小和 $克$局部离散空间的多项式次数。我们提供了验证理论的数值实验，并展示了该方法应用于稳态不可压缩 Navier-Stokes 方程时的性能。