Navier-斯托克斯方程时空有限元虚拟区域方法离散延拓的数值收敛性
Numerical convergence of discrete extensions in a space-time finite element, fictitious domain method for the Navier-Stokes equations
摘要：
作为虚拟区域的一个重要组成部分，高阶时空切割有限元（CutFEM）方法在演化区域上求解不可压斯托克斯方程（参见\“时空切割有限元法\”）。\cite{Bause2021}）是从时间相关的流域$Ω_f^t$到整个时间无关的计算域$Ω$的物理解的扩展。的扩展是隐式定义的，同时，旨在稳定的离散解的情况下，不可避免的不规则的小切口。在这里，该计划的收敛性数值研究的变化相结合的扩展和稳定。
英文摘要：
A key ingredient of our fictitious domain, higher order space-time cut finite element (CutFEM) approach for solving the incompressible Navier--Stokes equations on evolving domains (cf.\ \cite{Bause2021}) is the extension of the physical solution from the time-dependent flow domain $Ω_f^t$ to the entire, time-independent computational domain $Ω$. The extension is defined implicitly and, simultaneously, aims at stabilizing the discrete solution in the case of unavoidable irregular small cuts. Here, the convergence properties of the scheme are studied numerically for variations of the combined extension and stabilization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
