A Finite Element-Capacitance Matrix Method for the Neumann Problem for Laplace’s Equation

Capacitance matrix methods extend the usefulness of fast Poisson solvers to an important family of elliptic problems on arbitrary bounded regions. New algorithms of this kind are introduced for finite element approximations. The use of these methods for the Neumann problem for Laplace’s equation and important issues of implementation are discussed in some detail. It is shown that the new methods offer considerable advantages in comparison with finite difference–capacitance matrix methods previously employed.