Computation of volume potentials over bounded domains via approximate approximations
- Lanzara, Flavia
- Maz'ya, Vladimir
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 41A30 65D30 41A63 41A25
- Cubature of volume potentials, multivariate approximation, bounded domain
We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence.
- J. Math. Sci. (N. Y.), 189 (2013) pp. 508--524.