A two-dimensional moving finite element method with local refinement based on a posteriori error estimates

  title={A two-dimensional moving finite element method with local refinement based on a posteriori error estimates},
  author={Jens Lang and Weiming Cao and Weizhang Huang and Robert D. Russell},
  journal={Applied Numerical Mathematics},
In this paper, we consider the numerical solution of time-dependent PDEs using a finite element method based upon rh-adaptivity. An adaptive horizontal method of lines strategy equipped with a posteriori error estimates to control the discretization through variable time steps and spatial grid adaptations is used. Our approach combines an r-refinement method based upon solving so-called moving mesh PDEs with h-refinement. Numerical results are presented to demonstrate the capabilities and… 
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