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.

引用

页码：211 / 233

页数：23

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