Capacitance matrix method for petrov-galerkin procedure

In this paper a capacitance matrix method is developed for the Poisson equation on a rectangle $$ (1-1) Lu \equiv -(u_{xx} + u_{yy} = f, (x, y) \in \Omega \equiv (0, 1) \times (0, 1) $$ with the homogeneous Dirichlet boundary condition $$ (1-2) u = 0, (x, y) \in \partial\Omega $$ where $\partial\Omega$ is the boundary of the region $\Omega$.