Adaptive model refinement techniques

The adaptive model refinement techniques, also called bridging scale/ multigrid methods, are based on the idea of covering the entire computational... 

Bieniasz LK (2000) Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations. Part 5. A finite-difference adaptive space/time strategy based on a patch-type local uniform grid refinement, for kinetic models in one-dimensional space geometry. J Electroanal Chem 481 115-133. Corrigendum ibid. 565 131 (2004)... 

The roots of the Muschelknautz method ( MM ) extend back to the early work performed by Professor W. Barth (see Barth (1956), for example) of the University of Karlsruhe. Over the years, as understanding of the underlying phenomena and measuring techniques developed, Muschelknautz and co-workers, and those who have now followed him, have continued to refine the model. The reader of the literature will thus encounter many versions or improvements of the MM depending on the time of publication. It will also be noted that the more recent adaptations of the basic method are rather complex. We present some elements from simpler versions of the MM in other chapters (5 and 9) in this chapter and in Appendix 6.B we present what we believe to be a rather complete account of a later version of the model. Even here, however, we are obliged to strike a balance between covering all the details of the most recent versions of the MM, which would require another book in itself to do justice to all the details, and covering only the most basic elements of the model, which would limit its applicability or utility to the reader. 

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