圆盘上积分分数拉普拉斯扩散反应方程的谱伽辽金方法的尖锐误差估计

Math. Comput. Model. Pub Date : 2021-03-11 DOI:10.1090/MCOM/3645

Zhaopeng Hao, Hui-yuan Li, Zhimin Zhang, Zhongqiang Zhang

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引用次数: 6

摘要

研究了圆盘上二维分数阶扩散反应方程的谱伽辽金方法。首先证明了加权Sobolev空间中解的正则性估计。然后得到了分数阶扩散反应方程在l2 L^2和能量范数下的谱伽辽金方法的最优收敛阶。我们给出了数值结果来验证理论分析。

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Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk

We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-reaction equations on a disk. We first prove regularity estimates of solutions in the weighted Sobolev space. Then we obtain optimal convergence orders of a spectral Galerkin method for the fractional diffusion-reaction equations in the L 2 L^2 and energy norm. We present numerical results to verify the theoretical analysis.

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Math. Comput. Model.

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