Summary
The Cahn-Hilliard equation is of importance in materials science and a range of other fields. It represents a diffuse interface model for simulating the evolution of phase separation in solids and fluids, and is a nonlinear fourth-order parabolic equation, which makes its numerical solution particularly challenging. To this end, a finite element formulation has been developed which can solve the Cahn-Hilliard equation in its primal form using C° basis functions. Here, analysis of a fully discrete version of this method is presented in the form of a priori uniqueness, stability and error analysis.
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Wells, G.N., Garikipati, K. (2007). Analysis of a finite element formulation for modelling phase separation. In: Combescure, A., De Borst, R., Belytschko, T. (eds) IUTAM Symposium on Discretization Methods for Evolving Discontinuities. IUTAM Bookseries, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6530-9_5
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DOI: https://doi.org/10.1007/978-1-4020-6530-9_5
Publisher Name: Springer, Dordrecht
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