The article is concerned with and analyzes the α-robust error bound for time-fractional diffusion wave equations with weakly singular solutions. Nonuniform L1-type time meshes are used to handle non-smooth systems, and the sum-of-exponentials (SOEs) approximation for the kernels function is adopted to reduce the memory storage and computational cost. Meanwhile, the virtual element method (VEM), which can deal with complex geometric meshes and achieve arbitrary order of accuracy, is constructed for spatial discretization. Based on the explicit factors and discrete complementary convolution kernels, the optimal error bound of the fully discrete SOEs-VEM scheme in the L2-norm is derived in detail and that is α-robust, i.e., the bounds will not explosive growth while α→2−. Finally, some numerical experiments are implemented to verify the theoretical results.

中文翻译：

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时间分数扩散波方程的虚拟元方法的快速评估和稳健误差分析


本文关注并分析了具有弱奇异解的时间分数扩散波动方程的α鲁棒误差边界。非均匀 L1 型时间网格用于处理非平滑系统，内核函数采用指数和 （SOE） 近似来降低内存存储和计算成本。同时，构建了可以处理复杂几何网格并实现任意精度阶数的虚元方法 （VEM） 用于空间离散化。基于显式因子和离散互补卷积核，详细推导了 L2 范数中全离散 SOEs-VEM 方案的最优误差边界，即α稳健，即边界在 α→2− 时不会爆炸性增长。最后，通过一些数值实验验证了理论结果。