AMR vs High Order Schemes Wavelets as a Guide

The final goal behind any numerical method is give the smallest wall-clock time for a given final time error or, conversely, the smallest run-time error for a given wall clock time, etc. Here a comparison will be given between adaptive mesh refinement schemes and non-adaptive schemes of higher order. It will be shown that in three dimension calculations that in order for AMR schemes to be competitive that the finest scale must be restricted to an extremely, and unrealistic, small percentage of the computational domain