Fully discrete best-approximation-type estimates in L∞ (I;L2(ω)d) for finite element discretizations of the transient Stokes equations

被引：3
作者：
Behringer, Niklas [1 ]
Vexler, Boris [1 ]
Leykekhman, Dmitriy
机构：
[1] Tech Univ Munich, Ctr Math Sci, D-85748 Garching, Germany
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2023年 / 43卷 / 02期
关键词：
transient Stokes; discontinuous Galerkin method; finite elements; best approximation; pointwise error estimates; a priori estimates; PARABOLIC PROBLEMS; REGULARITY; POINTWISE; STABILITY; GRADIENT;
D O I：
10.1093/imanum/drac009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：852 / 880
页数：29
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