Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains

被引：16

作者：

Gu, Yiqi ^{[1
]}

Shen, Jie ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2020年 / 83卷 / 03期

关键词：

Spectral method; Petrov-Galerkin; Fictitious domain; Elliptic PDE; Error analysis; GALERKIN METHOD; DIRECT SOLVERS; EQUATIONS; PENALIZATION; SIMULATION; 2ND-ORDER;

D O I：

10.1007/s10915-020-01226-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop accurate and efficient spectral methods for elliptic PDEs in complex domains using a fictitious domain approach. Two types of Petrov-Galerkin formulations with special trial and test functions are constructed, one is suitable only for the Poisson equation but with a rigorous error analysis, the other works for general elliptic equations but its analysis is not yet available. Our numerical examples demonstrate that our methods can achieve spectral convergence, i.e., the convergence rate only depends on the smoothness of the solution.

引用

页数：20

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