A fourth-order accurate local refinement method for Poisson's equation

We present a block-structured local refinement method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume local refinement discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.