OPTIMAL REGULARITY AND ERROR ESTIMATES OF A SPECTRAL GALERKIN METHOD FOR FRACTIONAL ADVECTION-DIFFUSION-REACTION EQUATIONS

被引：49
|
作者：
Hao, Zhaopeng [1 ]
Zang, Zhongqiang [1 ]
机构：
[1] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2020年 / 58卷 / 01期
关键词：
regularity; pseudo-eigenrelation; weighted Sobolev spaces; fast solver with quasi-linear complexity; optimal error estimates; fractional Laplacian; spectral methods; NUMERICAL-METHODS; PART I; LAPLACIAN; DOMAINS; SPACES;
D O I：
10.1137/18M1234679
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate a spectral Galerkin method for the fractional advection-diffusion-reaction equations in one dimension. We first prove sharp regularity estimates of solutions in non-weighted and weighted Sobolev spaces. Then we obtain optimal convergence orders of the spectral Galerkin methods for both fractional advection-diffusion and diffusion-reaction equations. We also present an iterative solver with a quasi-optimal complexity. Numerical results are presented to verify the theoretical analysis.
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页码：211 / 233
页数：23
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