发表机构
Tongji University; University of Nevada Las Vegas; Shenzhen Raymind Biotechnology Co., Ltd.（同济大学; 内华达大学拉斯维加斯分校; 深圳锐明生物科技有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对移动界面两相Stokes流问题，提出并分析基于ALE的混合有限元方法，通过特定H^1投影获得半离散和全离散格式的最优误差估计，并推广至更一般情形。
AI 中文摘要
本文在整体（monolithic）框架下，针对一类具有移动界面和跳跃系数的两相Stokes流问题，发展和研究了一种基于任意拉格朗日-欧拉（ALE）的有限元方法（FEM）。基于ALE公式，建立了Stokes移动界面问题的混合有限元逼近，并在半离散和全离散格式下进行了分析。关键分析技术涉及一个与ALE引起的网格运动（由于界面演化）相关的特定H^1投影。证明了所提出的H^1投影及其ALE时间导数在H^1和L^2范数下的最优收敛性质，并由此获得了所研究的Stokes移动界面问题的半离散和全离散混合有限元逼近在H^1和L^2范数下的最优误差估计。进行了数值实验以验证所有推导的理论结果。所发展的分析方法可推广到Taylor-Hood和MINI混合元，以及更一般的两相流问题。
英文摘要
In this paper, an arbitrary Lagrangian-Eulerian (ALE)-based finite element method (FEM) is developed and studied in a monolithic framework for a class of two-phase Stokes flow problems with moving interfaces and jump coefficients, where the mixed finite element approximation to Stokes moving interface problems is established and analyzed in both semi- and fully discrete schemes based on the ALE formulation. The key analytical technique involves a specific H^1-projection associated with the ALE-induced mesh motion due to the evolving interface. Optimal convergence properties of the proposed H^1-projection and its ALE temporal derivative are proved in both H^1 and L^2 norms, with which optimal error estimates are obtained for both semi- and fully discrete mixed finite element approximations to the studied Stokes moving interface problem in both H1 and L2 norms as well. Numerical experiments are carried out to validate all derived theoretical results. The developed analytical approach can be extended to Taylor-Hood and MINI mixed elements, as well as to more general two-phase flow problems.
Comments41 pages, 9 figures
