Unified Analysis of Finite Element Methods for Problems with Moving Boundaries

@article{Gawlik2015UnifiedAO,
  title={Unified Analysis of Finite Element Methods for Problems with Moving Boundaries},
  author={Evan S. Gawlik and Adrian J. Lew},
  journal={SIAM J. Numer. Anal.},
  year={2015},
  volume={53},
  pages={2822-2846}
}
We present a unified analysis of finite element methods for problems with prescribed moving boundaries. In particular, we study an abstract parabolic problem posed on a moving domain with prescribed evolution, discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times. The moving mesh is assumed to evolve smoothly in time, except perhaps at a finite number of remeshing times where the solution is transferred between finite… 
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