Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons

被引：0

作者：

Hongli Jia

Benyu Guo

机构：

[1] Shanghai Normal University,Department of Mathematics

[2] Donghua University,Department of Mathematics

[3] Shanghai Normal University,Department of Mathematics

[4] Scientific Computing Key Laboratory of Shanghai Universities,undefined

[5] Shanghai E-institute for Computational Science,undefined

来源：

Chinese Annals of Mathematics, Series B | 2010年 / 31卷

关键词：

Legendre quasi-orthogonal approximation; Petrov-Galerkin spectral element method; Mixed inhomogeneous boundary value problems; 65N35; 41A05; 41A10; 35J25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.

引用

页码：855 / 878

页数：23

共 16 条

[1]

Guo B. Y.(2000)Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations J. Math. Anal. Appl. 243 373-408

[2]

Guo B. Y.(2010)Spectral method on quadrilaterals Math. Comp. 79 2237-2264

[3]

Jia H. L.(2006)Optical spectral-Galerkin methods using generalized Jacobi polynomials J. Sci. Comp. 27 305-322

[4]

Guo B. Y.(2004)Jacobi approximations in non-uniformly Jacobi-Weighted Sobolev spaces J. Appl. Theo. 128 1-41

[5]

Shen J.(2003)Non-isotropic Jacobi spectral method Cont. Math. 329 157-164

[6]

Wang L. L.(2005)Error analysis of spectral method on a triangle Adv. Comp. Math. 128 1-24

[7]

Guo B. Y.(2009)Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an finite channel Math. Comp. 78 129-151

[8]

Wang L. L.(2010)Composite Laguerre-Legendre spectral method for exterior problems Adv. Comp. Math. 32 393-429

[9]

Guo B. Y.(undefined)undefined undefined undefined undefined-undefined

[10]

Wang L. L.(undefined)undefined undefined undefined undefined-undefined

← 1 2 →