"Approximate approximations" and the cubature of potentials
- Maz´ya, Vladimir
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 41A55 41A63 65D32
- Multivariate quasi-interpolation, Cubature formulas, Harmonic, elastic, diffraction potentials
The paper discusses new cubature formulas for classical integral operators of mathematical physics based on the "approximate approximation" of the density with Gaussian and related functions. We derive formulas for the cubature of harmonic, elastic and diffraction potentials approximating with high order in some range relevant for numerical computations. We prove error estimates and provide numerical results for the Newton potential.
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