A Fourth Order Accurate Adaptive Mesh Refinement Method for Poisson’s Equation

We present a block-structured adaptive mesh refinement (AMR) 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, with cell-centered discretizations of the right-hand side and the solution. This is combined with finite volume AMR discretizations based on flux matching on refinement boundaries to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.

This poster summarizes research conducted during the CSGF practicum experience.