标题： 时间依赖的斯托克斯方程在流函数形式下的有限元离散的全离散误差分析 显示英文标题

标题： Fully discrete error analysis of finite element discretizations of time-dependent Stokes equations in a stream-function formulation

摘要： 在本文中，我们利用流函数公式法，建立了时变斯托克斯问题全离散伽辽金解的最佳逼近型误差估计。 对于时间离散化，我们使用任意次数的不连续伽辽金方法，而空间离散化则在一个通用框架中进行。 这使得我们的结果适用于多种空间离散化方法，只要满足某些伽辽金正交性条件。 作为例子，符合的$C^1$和$C^0$内部惩罚方法被我们的分析所涵盖。 这些结果不需要超出由区域和数据给出的自然正则性的额外正则性假设，并可用于最优控制问题。 显示英文摘要

摘要： In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous Galerkin method of arbitrary degree, whereas we present the space discretization in a general framework. This makes our result applicable for a wide variety of space discretization methods, provided some Galerkin orthogonality conditions are satisfied. As an example, conformal $C^1$ and $C^0$ interior penalty methods are covered by our analysis. The results do not require any additional regularity assumptions beyond the natural regularity given by the domain and data and can be used for optimal control problems.