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We consider radially symmetric capillary surfaces that are described bybounded generating curves. We use the arc-length representation of thedifferential equations for these surfaces to allow for vertical points andinflection points along the generating curve. These considerations admitcapillary tubes, sessile drops, and fluids in annular tubes as well as otherexamples.  We present a multi-scale pseudo-spectral method for approximating solutionsof the associated boundary value problems based on interpolation by Chebyshevpolynomials. The multi-scale approach is based on a domain decomposition withadaptive refinements within each sub-domain.

Multi-scale spectral methods for bounded radially symmetric capillary surfaces