In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions.

翻译：在本篇文章中,我们获得了关于瞬时斯托克斯问题完全离散近似的最佳近似类型结果。在时间离散时,我们使用不连续的加列尔金方法和空间离散时,我们使用标准限量元素来解决斯托克斯问题,满足离散的内溢条件。分析使用离散的最大抛物线规律技术。结果只需要对数据进行自然假设,而不假定解决方案有任何额外的顺利性。