A two-dimensional multiterm fractional delay diffusion equation is considered. The representation of the exact solution of the equation is derived and it is shown that the solution exhibits singular behaviors at multiple nodes due to the initial singularity and time delay. This results in the numerical schemes for solving the equation typically have a lower order of convergence in time. The problem is approximated in time by the L1 and Alikhanov schemes on symmetrical graded meshes, while in space the standard finite element method is applied. Numerical stability and convergence are presented for the schemes. Numerical experiments are performed to show the effectiveness of the schemes.

中文翻译：

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二维多项分数延迟扩散方程的 L1-FEM 离散化


考虑二维多项分数延迟扩散方程。推导了方程精确解的表示形式，结果表明，由于初始奇异性和时间延迟，该解在多个节点处表现出奇异行为。这导致求解方程的数值方案通常具有较低的时间收敛阶数。该问题在时间上通过对称渐变网格上的 L1 和 Alikhanov 格式进行近似，而在空间上则应用标准有限元方法。给出了该方案的数值稳定性和收敛性。进行数值实验以显示该方案的有效性。