An adaptive multigrid tool for elliptic and parabolic systems

This paper describes a multigrid tool for use with adaptively refined meshes in two dimensions. A standard full approximation storage (FAS) multigrid scheme is modified to maintain efficient performance on non-uniform grids arising as a result of local mesh refinement. This is achieved by allowing hanging nodes to exist but ensuring that at each stage of the FAS algorithm the solution is projected into the continuous space in which the hanging node values are interpolants of their coarse grid parent values. A non-linear, elliptic, finite element example is provided to demonstrate the efficiency of the proposed algorithm. However, the method is also suitable for linear and non-linear parabolic problems.