Fully discrete best-approximation-type estimates in L ∞ ( I ; L 2(Ω) d ) for finite element discretizations of the transient Stokes equations
Fully discrete best-approximation-type estimates in L ∞ ( I ; L 2(Ω) d ) for finite element discretizations of the transient Stokes equations
复制标题
L ≤ ( I ; L 2(Î) d ) 中的完全离散最佳逼近型估计，用于瞬态 Stokes 方程的有限元离散化
DOI：
10.1093/imanum/drac009
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发表时间：
2022
影响因子：
2.1
通讯作者：
Leykekhman, Dmitriy
中科院分区：
文献类型：
--
作者：
Behringer, Niklas;Vexler, Boris;Leykekhman, Dmitriy
在本文中，我们得到了瞬态Stokes问题的全离散近似的最优逼近型结果。对于时间离散，我们采用不连续伽辽金方法；对于空间离散，我们采用标准有限元方法。分析采用离散极大抛物正则性技术。结果只需要对数据进行自然假设，而不假设解具有任何额外的平滑性。
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.