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    Approximation of linear partial differential equations on spheres

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    etd-tamu-2003B-2003062713-LE G-1.pdf (426.3Kb)
    Date
    2004-09-30
    Author
    Le Gia, Quoc Thong
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    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
    https://hdl.handle.net/1969.1/22
    Subject
    spherical basis functions
    partial differential equations
    numerical analysis
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    • Electronic Theses, Dissertations, and Records of Study (2002– )
    Citation
    Le Gia, Quoc Thong (2003). Approximation of linear partial differential equations on spheres. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /22.

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