|
Description:
|
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 . |