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On approximation classes for adaptive time-stepping finite element methods
IMA Journal of Numerical Analysis ( IF 2.3 ) Pub Date : 2022-09-16 , DOI: 10.1093/imanum/drac056
Marcelo Actis 1 , Pedro Morin 1 , Cornelia Schneider 2
Affiliation  

We study approximation classes for adaptive time-stepping finite element methods for time-dependent partial differential equations. We measure the approximation error in $L_2([0,T)\times \varOmega )$ and consider the approximation with discontinuous finite elements in time and continuous finite elements in space, of any degree. As a by-product we define anisotropic Besov spaces for Banach-space-valued functions on an interval and derive some embeddings, as well as Jackson- and Whitney-type estimates.

中文翻译:

关于自适应时间步进有限元方法的近似类

我们研究了时间相关偏微分方程的自适应时间步进有限元方法的近似类。我们测量 $L_2([0,T)\times \varOmega )$ 中的近似误差,并考虑任何程度的时间不连续有限元和空间连续有限元的近似。作为副产品,我们为区间上的 Banach 空间值函数定义各向异性 Besov 空间,并推导出一些嵌入,以及 Jackson 和 Whitney 类型的估计。
更新日期:2022-09-16
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