**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30827

##### A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

**Authors:**
Sheng-Gwo Chen,
Jyh-Yang Wu

**Abstract:**

**Keywords:**
Conservation Laws,
diffusion equations,
Cahn-Hilliard equations,
evolving surfaces

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1127164

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[3] S.-G. Chen and J.-Y. Wu, “Discrete conservation laws on curved surfaces”, SIAM J. Sci. Comput., vol. 35, 2013, pp. A719-A739.

[4] S.-G. Chen and J.-Y. Wu, “Discrete conservation laws on curved surfaces II: A dual approach”, SIAM J. Sci. Comput., vol. 36, 2014, pp. A1813-A1830.

[5] S.-G. Chen, M.-H. Chi, and J.-Y. Wu, “High-Order Algorithms for Laplace–Beltrami Operators and Geometric Invariants over Curved Surfaces”, vol 65, 2015, pp.839-865.

[6] S.-G. Chen and J.-Y. Wu, “Discrete conservation laws on evolving surfaces”, SIAM J. Sci. Comput., vol. 38, 2016, pp. A1725-A1742.

[7] M. DoCarmo, “Differential geometry of curves and surfaces, Prentice-Hall, Lodon, 1976.

[8] M. DoCarmo, “Riemannian geometry”, Birkhauser, Boston, 1992.

[9] I. Dolcetta, S. Vita, R. March, "Area-preserving curve-shortening flows: from phase separation to image processing", Interfaces Free Bound. vol. 4, 2002, pp. 325-343.

[10] Q. Dua, L. Ju and Li Tian, "Finite element approximation of the Cahn–Hilliard equation on surfaces", Comput. Methods Appl. Mech. Engrg., vol. 200, 2011, pp. 2458-2470.

[11] C. M. Elliott and T. Ranner, "Evolving surface finite element method for the Cahn–Hilliard equation", Numer. Math. vol.3, 2015, pp483-534.