Another exercise involves fixing the number of nodes to the maximum number and then moving the nodes so that they are positioned in the optimal locations (the so-called r method or relocation method). Still another possibility is to use an de-refinement strategy, in which regions of the discretized domain that were too finely meshed in the original mesh can be ``unrefined'' and help balance the total number of degrees of freedom. At some point, however, for most large three-dimensional problems, one must face the option of parallelizing the algorithms so that they can be run on either a distributed system of high-end workstations or a massively parallel machine. The use of such techniques for adaptive mesh generation is just in its infancy, but is certainly a topic of considerable importance to researchers who work on large-scale finite element systems.
To find out more about parallel adaptive refinement methods and adaptive methods in general, see [45,34,39,40,42].