Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation
Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction–Diffusion Equation
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DOI：
10.1007/s10915-018-0800-0
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发表时间：
2018-08
影响因子：
2.5
通讯作者：
Zhongqiang Zhang
中科院分区：
文献类型：
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作者：
Zhongqiang Zhang
考虑一维空间中一类带反应项的分数阶扩散方程.我们首先建立了加权Sobolev空间的正则性。然后我们给出了方程的谱Galerkin方法的最优误差估计和谱Petrov-Galerkin方法的次优误差估计。数值结果表明，对于光滑输入，在加权范数下的收敛阶为分数阶拉普拉斯算子的阶.
We consider a fractional diffusion equation with a reaction term in one dimensional space. We first establish the regularity in weighted Sobolev spaces. Then we present an optimal error estimate for a spectral Galerkin method for the equation and a sub-optimal error estimate for a spectral Petrov–Galerkin method. Numerical results suggest that the convergence order in a weighted-norm isfor smooth inputs whereis the order of the fractional Laplacian.