Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier–Stokes equations. The spatial discretization based on inf–sup stable pairs of finite element spaces is stabilized using a one-level local projection stabilization method. Optimal error bounds for the velocity with constants independent of the viscosity parameter are obtained for both the semidiscrete case and the fully discrete case. Numerical results support the theoretical predictions.

中文翻译：

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演化Navier–Stokes方程的高阶不连续Galerkin时间离散

高阶不连续Galerkin方法被用作瞬态Navier–Stokes方程的时间离散。使用一级局部投影稳定化方法来稳定基于inf–upup有限元空间对的空间离散化。对于半离散情况和完全离散情况，都获得了具有与粘度参数无关的常数的最佳速度误差范围。数值结果支持理论预测。