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

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

Received date: 2023-01-20

  Revised date: 2023-02-27

  Accepted date: 2023-03-03

  Online 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).

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.

Cite this article

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 . DOI: 10.1007/s42967-023-00269-7

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