This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundar...

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Bibliographic Details

Main Authors:	Eisenstat, Stanley S. (Author), Schreiber, Robert Samuel (Author), Schultz, Martin H. (Author)
Format:	Book
Language:	English
Published:	[New Haven, Conn.] 1977
Series:	Yale University <New Haven, Conn.> / Department of Computer Science: Research report 109
Subjects:	Galerkin method Rayleigh ritz method Approximation(mathematics) Boundary value problems Computations Ellipses Finite element analysis Partial differential equations Polynomials Splines(geometry) Theoretical Mathematics
Summary:	This paper considers the numerical solution of elliptic partial differential equations in spherical domains. When all the functions involved are spherically symmetric (that is, they depend only on distance from the center of the domain), the problem can be replaced by an equivalent two-point boundary value problem. The resulting problem is singular, but nevertheless has a smooth solution. It should therefore be possible to approximate the solution accurately using the Rayleigh-Ritz Galerkin method with a piecewise polynomial subspace on a quasiuniform mesh. Optimal-order error bounds will be obtained, showing that this procedure is theoretically well-founded. Instead of the usual Sobolev norms, norms are used which are appropriate to the original n-dimensional setting of the problem.