A comparison of some adaptive space mesh solvers for the numerical solution of parabolic partial differential equations

We examine a number of adaptive space mesh routines which were designed to provide accurate numerical approximations to the solutions of parabolic partial differential equations in one space dimension. Both static and dynamic regridding techniques are considered, and in numerical experiments, we compare their relative performances by measuring a range of statistics including accuracy and cpu when applied to approximate the solutions of a set of representative test problems.