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Analysis of a finite element formulation for modelling phase separation

By G N Wells and Krishna Garikipati

Abstract

In Combescure, A., De Borst, R., and Belytschko, T., editors, IUTAM Symposium on Discretization Methods for Evolving Discontinuities, volume 5 of IUTAM Bookseries, pages 89–102. Springer.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^0 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

Topics: Cahn-Hilliard equation, discontinuous Galerkin method, phase separation
Publisher: Springer
Year: 2007
OAI identifier: oai:www.repository.cam.ac.uk:1810/221727
Provided by: Apollo

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Citations

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