Stability and error estimates for a projection based variational multiscale finite element scheme for Oseen problem in a time-dependent domain are derived in this paper. The use of Geometric Conservation Law (GCL) provides an unconditional stable scheme, whereas a restriction on the time-step needs to be imposed to obtain stability estimates independent of the mesh velocity when GCL is violated. Further, a priori error estimate is derived for the semi-discrete problem obtained with the backward Euler time discretization.

中文翻译：

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基于投影的时变域中Oseen问题的变分多尺度有限元方法的先验误差分析

本文推导了基于投影的时变域中Oseen问题的变分多尺度有限元格式的稳定性和误差估计。几何守恒定律（GCL）的使用提供了无条件的稳定方案，而在违反GCL时，需要对时间步长进行限制以获得独立于网格速度的稳定性估计。此外，针对通过后向欧拉时间离散化获得的半离散问题得出先验误差估计。