非定常渗透对流模型的二阶BDF有限元算法的误差分析

Optimal Error Estimate of Second-order BDF Finite Element Schemes for Unsteady Penetrative Convection Model

研究了非定常渗透对流模型的全离散化的二阶BDF有限元算法,提出并分析了基于外推的线性化全离散方案,证明了该方程组离散解的稳定性,通过对误差函数利用能量估计方法,结合有限元逆不等式和Sobolev空间的插值不等式,得到了无条件的最优L2误差估计.

This paper studies the fully discretized second-order BDF finite element algorithm of the unsteady penetrative convection model, puts forward and analyzes the discretization scheme based on linear extrapolation, and proves the stability of discrete solution to the system. Based on the theoretical analysis of the energy estimate of the error function and using finite element inverse and interpolation inequality in Sobolev space, we obtain the unconditional optimal L2 error estimation.