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Approximation of linear partial diff...

Le Gia, Quoc Thong.

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Approximation of linear partial differential equations on spheres.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Approximation of linear partial differential equations on spheres./
Author:	Le Gia, Quoc Thong.
Description:	117 p.
Notes:	Chairs: Joseph D. Ward; Francis J. Narcowich.
Contained By:	Dissertation Abstracts International64-09B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3104008
ISBN:	9780496515769

Approximation of linear partial differential equations on spheres.
Le Gia, Quoc Thong.

Approximation of linear partial differential equations on spheres. - 117 p.

Chairs: Joseph D. Ward; Francis J. Narcowich.

Thesis (Ph.D.)--Texas A&M University, 2003.

The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both the finite element method and the collocation method are discussed. In the heat equation, only the collocation method is considered. Error estimates in the supremum norms and the Sobolev norms are obtained when certain regularity conditions are imposed on the spherical basis functions.

ISBN: 9780496515769Subjects--Topical Terms:

515831
Mathematics.

Approximation of linear partial differential equations on spheres.
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008 110524s2003 ||||||||||||||||| ||eng d
020 $a 9780496515769
035 $a (UMI)AAI3104008
035 $a AAI3104008
040 $a UMI $c UMI
100 1 $a Le Gia, Quoc Thong. $3 1271960
245 1 0 $a Approximation of linear partial differential equations on spheres.
300 $a 117 p.
500 $a Chairs: Joseph D. Ward; Francis J. Narcowich.
500 $a Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4400.
502 $a Thesis (Ph.D.)--Texas A&M University, 2003.
520 $a The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both the finite element method and the collocation method are discussed. In the heat equation, only the collocation method is considered. Error estimates in the supremum norms and the Sobolev norms are obtained when certain regularity conditions are imposed on the spherical basis functions.
590 $a School code: 0803.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Texas A&M University. $3 718977
773 0 $t Dissertation Abstracts International $g 64-09B.
790 $a 0803
790 1 0 $a Narcowich, Francis J., $e advisor
790 1 0 $a Ward, Joseph D., $e advisor
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3104008