Analysis of finite element approximations of a phase field model for two-phase fluids

@article{Feng2007AnalysisOF,
  title={Analysis of finite element approximations of a phase field model for two-phase fluids},
  author={Xiaobing Feng and Yinnian He and Chun Liu},
  journal={Math. Comput.},
  year={2007},
  volume={76},
  pages={539-571}
}
This paper studies a phase field model for the mixture of two immiscible and incompressible fluids. The model is described by a nonlinear parabolic system consisting of the nonstationary Stokes equations coupled with the Allen-Cahn equation through an extra phase induced stress term in the Stokes equations and a fluid induced transport term in the Allen-Cahn equation. Both semi-discrete and fully discrete finite element methods are developed for approximating the parabolic system. It is shown… CONTINUE READING
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