Approximation of linear partial differential equations on spheres

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Title: Approximation of linear partial differential equations on spheres
Author: Le Gia, Quoc Thong
Abstract: 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 .
URI: http : / /hdl .handle .net /1969 .1 /22
Date: 2004-09-30

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Approximation of linear partial differential equations on spheres. Available electronically from http : / /hdl .handle .net /1969 .1 /22 .

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