Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem
Min Cao , Yuan Li
Communications on Applied Mathematics and Computation ›› : 1 -25.
Optimal Error Analysis of Linearized Crank-Nicolson Finite Element Scheme for the Time-Dependent Penetrative Convection Problem
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 $L^2$-norm are derived. Finally, numerical results are presented to confirm the theoretical analysis.
National Natural Science Foundation of China(11771337)
Natural Science Foundation of Zhejiang Province(LY23A010002)
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