Error analysis of a mixed finite element method for the Cahn-Hilliard equation

@article{Feng2004ErrorAO,
  title={Error analysis of a mixed finite element method for the Cahn-Hilliard equation},
  author={Xiaobing Feng and Andreas Prohl},
  journal={Numerische Mathematik},
  year={2004},
  volume={99},
  pages={47-84}
}
We propose and analyze a semi-discrete and a fully discrete mixed finite element method for the Cahn-Hilliard equation ut + (ε u− ε−1f (u)) = 0, where ε > 0 is a small parameter. Error estimates which are quasi-optimal order in time and optimal order in space are shown for the proposed methods under minimum regularity assumptions on the initial data and the domain. In particular, it is shown that all error bounds depend on 1 ε only in some lower polynomial order for small ε. The cruxes of our… CONTINUE READING

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