**Preprint series:** 10-01, Reports on Numerical Mathematics

**MSC:**- 35J20 Variational methods for second-order, elliptic equations
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

**Abstract:** By using Kelvin's inversion, we construct analytical harmonic functions satisfying the zero-Neumann condition on the inner spherical wall everywhere except a single point where the velocity is infinite. This set of functions can be used to construct approximate velocity potentials associated with liquid sloshing in a spherical tank, and in other related hydrodynamic problems.

**Keywords:** *Sloshing, spherical tank, variational methods, modal system*

**Upload:** 2010-04-16

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