Analysis of Continuous Moving Mesh

@inproceedings{Smith1996AnalysisOC,
  title={Analysis of Continuous Moving Mesh},
  author={E. H. Smith and USAAndrew M. Stuart},
  year={1996}
}
We consider a continuous formulation of moving mesh equations based on a relaxation of an equidistribution principle. Under natural assumptions on the monitor function, we derive bounds on the departure from equidistribution of the evolving mesh. Furthermore, we derive stability bounds for solutions of the equations based on the stability of the underlying PDE. Numerical examples are given to illustrate the behavior of such methods in practice. 

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