Periodic Dirac delta distributions in the boundary element method (Q1610206)

The authors analyse the Dirac delta methods defined on equally spaced grids for a class of pseudodifferential equations of negative or zero order. Asymptotic expansions of the error are obtained for delta-spline and delta-delta methods. As a byproduct the authors obtain the existence of asymptotic expansions of the nodal error and of the error under some linear postprocessing, including potentials in the boundary element method. The rate of convergence with respect to the position of the nodes with reference to the testing grid is also investigated.