2012/10/26 by Flavia Lanzara, Lanzara, F., Vladimir Maz’ya +3
Mathematics · Engineering · #Mathematical Approximation and Integration #Advanced Numerical Methods in Computational Mathematics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1210.7084
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.