In the past, the CVBEM (complex variable boundary element method) has
been approached as a collocation problem or by least squares. In this
work, the CVBEM analog is redeveloped as a series expansion of nodal p
oint functions with unknown nodal point values as the coefficients. Th
is series expansion provides further insight into the theoretical and
approximation aspects of the CVBEM. Applications demonstrate the utili
ty of the CVBEM as a computational approach to solving two-dimensional
potential problems involving Laplace and Poisson equations.