Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem

doi:10.1007/s42967-023-00269-7

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (1): 264-288.doi: 10.1007/s42967-023-00269-7

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Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem

Min Cao, Yuan Li

College of Mathematics and Physics, Wenzhou University, Chashan, Wenzhou 325035, Zhejiang, China

收稿日期:2023-01-20 修回日期:2023-02-27 接受日期:2023-03-03 出版日期:2025-04-21 发布日期:2025-04-21
通讯作者: Yuan Li,liyuan@wzu.edu.cn E-mail:liyuan@wzu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (No. 11771337) and the Natural Science Foundation of Zhejiang Province of China (No. LY23A010002).

Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem

Min Cao, Yuan Li

College of Mathematics and Physics, Wenzhou University, Chashan, Wenzhou 325035, Zhejiang, China

Received:2023-01-20 Revised:2023-02-27 Accepted:2023-03-03 Online:2025-04-21 Published:2025-04-21
Supported by:
This work was supported by the National Natural Science Foundation of China (No. 11771337) and the Natural Science Foundation of Zhejiang Province of China (No. LY23A010002).

摘要/Abstract

摘要： This paper focuses on the optimal error analysis of a linearized Crank-Nicolson finite element scheme for the time-dependent penetrative convection problem, where the mini element and piecewise linear finite element are used to approximate the velocity field, the pressure, and the temperature, respectively. We proved that the proposed finite element scheme is unconditionally stable and the optimal error estimates in L²-norm are derived. Finally, numerical results are presented to confirm the theoretical analysis.

关键词: Time-dependent penetrative convection problem, Linearized Crank-Nicolson scheme, Finite element method, Error estimate

Abstract: This paper focuses on the optimal error analysis of a linearized Crank-Nicolson finite element scheme for the time-dependent penetrative convection problem, where the mini element and piecewise linear finite element are used to approximate the velocity field, the pressure, and the temperature, respectively. We proved that the proposed finite element scheme is unconditionally stable and the optimal error estimates in L²-norm are derived. Finally, numerical results are presented to confirm the theoretical analysis.

Key words: Time-dependent penetrative convection problem, Linearized Crank-Nicolson scheme, Finite element method, Error estimate

中图分类号:

Min Cao, Yuan Li. Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem[J]. Communications on Applied Mathematics and Computation, 2025, 7(1): 264-288.

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Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem

Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem

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