An adaptive high-order unfitted finite element method for elliptic interface problems

Chen Zhiming; Li Ke; Xiang Xueshuang

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An adaptive high-order unfitted finite element method for elliptic interface problems

机译：椭圆界面问题的自适应高阶非拟合有限元方法

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摘要

We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse estimate which allows us to prove the stability of the finite element method under practical interface resolving mesh conditions and also prove the lower bound of the hp a posteriori error estimate. Numerical examples are included.

机译：我们在具有悬挂节点的笛卡尔网格上设计了一种自适应非拟合有限元方法。我们推导了 K 网格上 hp 可靠且高效的残差 A 型后验误差估计。一个关键因素是新颖的hp域逆估计，它使我们能够证明有限元方法在实际界面解析网格条件下的稳定性，并证明hp的下界是后验误差估计。包括数值示例。

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来源
《Numerische Mathematik》 |2021年第3期|507-548|共42页
作者
Chen Zhiming; Li Ke; Xiang Xueshuang;
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作者单位

Chinese Acad Sci;

Univ Chinese Acad Sci;

China Acad Space Technol;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
65N30; DISCONTINUOUS GALERKIN METHODS; POSTERIORI ERROR ESTIMATION; CONVERGENCE; EQUATIONS; APPROXIMATION; INTERPOLATION; ESTIMATORS; FLOW; NORM;

机译：65N30;非连续伽乐氏金方法;后验误差估计;收敛;方程式;近似值;插值;估算器;流程;规范;

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3. Corrected finite element methods on unfitted meshes for Stokes moving interface problem [J] . Laymuns Genaro, Sanchez Manuel A. Computers & Mathematics with Applications: An International Journal . 2022,第15期

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4. Mathematical Modeling of Composite and Inhomogeneous Deformable Materials Based on Scanning and Finite Element Method [C] . Pykhalov A. A., Duong V. L., Zotov I. N. International Conference on Aviamechanical Engineering and Transport . 2019

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5. Finite Element Method of Incompressible Viscous Fluid Flow by Means of Perturbation Method (有限要素法の数学的基礎理論) [O] . KAWAHARA MUTSUTO 1975

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6. DATA INPUT MANUAL FOR RSI/TEVCO: A THERMO/VISCOELASTIC FINITE ELEMENT COMPUTER PROGRAM [R] . Gary D. Callahan, Arlo F. Fossum 1977

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An adaptive high-order unfitted finite element method for elliptic interface problems

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