Summary
A fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analysed. Existence and uniqueness of the numerical solution and its convergence to the solution of the continuous problem are proved. Two iterative schemes to solve the resulting algebraic problem are proposed and some numerical results in one space dimension are presented.
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Copetti, M.I.M., Elliott, C.M. Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Numer. Math. 63, 39–65 (1992). https://doi.org/10.1007/BF01385847
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DOI: https://doi.org/10.1007/BF01385847