Cubature rules for harmonic functions based on Radon projections

We construct a class of cubature formulae for harmonic functions on the unit disk based on line integrals over distinct chords. These chords are assumed to have constant distance to the center of the disk, and their angles to be equispaced over the interval . If is chosen properly, these formulae integrate exactly all harmonic polynomials of degree up to , which is the highest achievable degree of precision for this class of cubature formulae. For more generally distributed chords, we introduce a class of interpolatory cubature formulae which we show to coincide with the previous formulae for the equispaced case. We give an error estimate for a particular cubature rule from this class and provide numerical examples.