A priori error bounds on potentials, fields, and energies evaluated with a modified kernel

The singular integrals involved in the solution of the scalar and vector Poisson equation are considered. A regularization method, which depends on a positive parameter, is described. The dependence of the error on the value of the positive parameter is studied. An a priori upper bound on the error is calculated, which can be used when applying the method in solving general three-dimensional problems by means of integral methods.