Object-oriented hierarchical mesh refinement with CHARMS

A new approach to the construction of adaptive approximations on finite element meshes and also in more general settings, including approximations on subdivision surfaces, had been recently proposed by Krysl, Grinspun, and Schröder. This paper outlines how the general refinement algorithms may be specialized to some common finite element discretizations in two and three dimensions, discusses the design of nested meshes, and delves into the algorithmic, design, and implementation issues in an object oriented software framework (http://hogwarts.ucsd.edu/∼pkrysl/CHARMS