论文标题
与内存的kirchhoff类型quasilInear Supdiffusion的线性分数曲柄nicolson Fem的错误估计值
Error Estimates for a Linearized Fractional Crank-Nicolson FEM for Kirchhoff type Quasilinear Subdiffusion Equation with Memory
论文作者
论文摘要
在本文中，我们为Kirchhoff类型的quasilIrInear时间折叠式差异方程$ \ left（\ Mathcal {d}^α\ right）$开发了一个线性化的曲柄曲柄 - nicolson-galerkin fem。通常，时间分数问题的解决方案在时间时表现出较弱的奇异性$ t = 0 $。在得出开发的数值方案的收敛估计的同时，考虑了解决方案的这种单数行为。我们证明，提出的数值方案的准确率为$ O（m^{ - 1}+n^{ - 2}）$ in $ l^{\ infty}（0，t; t; l^{2}（ω））$，以及$ l^{\ infty}（0，t;是空间和时间方向上的自由度。提出了一个数值实验，以验证理论结果。
In this paper, we develop a linearized fractional Crank-Nicolson-Galerkin FEM for Kirchhoff type quasilinear time-fractional integro-differential equation $\left(\mathcal{D}^α\right)$. In general, the solutions to the time-fractional problems exhibit a weak singularity at time $t=0$. This singular behavior of the solutions is taken into account while deriving the convergence estimates of the developed numerical scheme. We prove that the proposed numerical scheme has an accuracy rate of $O(M^{-1}+N^{-2})$ in $L^{\infty}(0,T;L^{2}(Ω))$ as well as in $L^{\infty}(0,T;H^{1}_{0}(Ω))$, where $M$ and $N$ are the degrees of freedom in the space and time directions respectively. A numerical experiment is presented to verify the theoretical results.
