Optimal convergence of arbitrary Lagrangian-Eulerian iso-parametric finite element methods for parabolic equations in an evolving domain

被引：2
|
作者：
Li, Buyang [1 ]
Xia, Yinhua [2 ]
Yang, Zongze [1 ]
机构：
[1] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Hong Kong, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2023年 / 43卷 / 01期
基金：
中国国家自然科学基金;
关键词：
arbitrary Lagrangian-Eulerian; evolving domain; parabolic equation; finite element method; iso-parametric; DISCONTINUOUS GALERKIN METHOD; CONSERVATION-LAWS; STABILITY;
D O I：
10.1093/imanum/drab099
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An optimal-order error estimate is presented for the arbitrary Lagrangian-Eulerian (ALE) finite element method for a parabolic equation in an evolving domain, using high-order iso-parametric finite elements with flat simplices in the interior of the domain. The mesh velocity can be a linear approximation of a given bulk velocity field or a numerical solution of the Laplace equation with specified boundary value matching the velocity of the boundary. The optimal order of convergence is obtained by comparing the numerical solution with the ALE-Ritz projection of the exact solution, and by establishing an optimal-order estimate for the material derivative of the ALE-Ritz projection error.
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页码：501 / 534
页数：34
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