Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and Its Fully Discrete Finite Element Approximation

@article{Feng2012AnalysisOA,
  title={Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and Its Fully Discrete Finite Element Approximation},
  author={Xiaobing Feng and Steven M. Wise},
  journal={SIAM J. Numerical Analysis},
  year={2012},
  volume={50},
  pages={1320-1343}
}
In this paper we present PDE and finite element analyses for a system of PDEs consisting of the Darcy equation and the Cahn–Hilliard equation, which arises as a diffuse interface model for the two-phase Hele-Shaw flow. In the model the two sets of equations are coupled through an extra phase induced force term in the Darcy equations and a fluid induced transport term in the Cahn–Hilliard equation. We propose a fully discrete implicit finite element method for approximating the PDE system, which… CONTINUE READING
24 Citations
24 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 24 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Modeling pinch-off and reconstruction in a Hele-Shaw cell

  • H.-G. Lee, J. Lowengrub, J. Goodman
  • I. The analysis and simulation in the nonlinear…
  • 2002
Highly Influential
7 Excerpts

Phase field models of solidification

  • G. B. McFadden
  • Contemp. Math., 295
  • 2002
Highly Influential
4 Excerpts

Sobolev Spaces

  • R. A. Adams
  • Academic Press, New York
  • 1975
Highly Influential
6 Excerpts

Numerical analysis of the Cahn-Hilliard equation and approximation for the Hele-Shaw problem

  • X. Feng, A. Prohl
  • Interfaces Free Bound., 7
  • 2005
1 Excerpt

Similar Papers

Loading similar papers…