An approximate factorization/least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
This paper deals with the numerical solution of the Cahn-Hilliard equation. A mixed formulation making possible the approximation of the problem \[ \frac{\partial u}{\partial t}- \Delta(u^3-u)+ \varepsilon^2\Delta^2u=0 \quad\text{in }\Omega\times (0,T), \] \[ u(x,0)= u_0(x), \quad x\in\Omega, \quad \frac{\partial u}{\partial n}=\frac{\partial}{\partial n}\Delta u=0\quad\text{on }\partial\Omega, \] by finite element techniques traditionally used for the approximation of second-order elliptic or parabolic problems is combined with a least squares formulation based on an approximate factorization of a fourth-order elliptic operator which appears in the numerical model. The authors have visualized the computed solutions of two problems to illustrate the possibilities of the presented methods.
scientific article; zbMATH DE number 1000125
scientific article