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

doi:10.1007/s42967-023-00269-7

Abstract

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

CLC Number:

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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