The solutions of the nonlinear time fractional parabolic problems usually undergo dramatic changes at the beginning. In order to overcome the initial singularity, the temporal discretization is done by using the Alikhanov schemes on the nonuniform meshes. And the spatial discretization is achieved by using the finite element methods. The optimal error estimates of the fully discrete schemes hold without certain time-step restrictions dependent on the spatial mesh sizes. Such unconditionally optimal convergent results are proved by taking the global behavior of the analytical solutions into account. Numerical results are presented to confirm the theoretical findings.

中文翻译：

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非线性时间分数阶抛物方程的非均匀Alikhanov线性化Galerkin有限元方法

非线性时间分数抛物线问题的解通常在开始时就发生巨大变化。为了克服初始奇点，通过在非均匀网格上使用Alikhanov方案进行时间离散化。并通过有限元方法实现空间离散化。完全离散方案的最佳误差估计不受空间网格大小的影响而不受某些时间步长的限制。通过考虑解析解的整体行为，证明了这种无条件的最优收敛结果。数值结果证实了理论发现。