A discontinuous Galerkin method for the Cahn-Hilliard equation (Q5919959)

The paper deals with the viscous Cahn-Hilliard equation \[ u_t - \delta u_{txx} + \alpha u_{xxxx} = (\phi(u))_{xx},\quad x \in \Omega, \;t>0, \] with initial condition \[ u(x,0) = u_0(x), \;x \in \Omega, \] and boundary condition \[ u_x = u_{xxx} = 0, \quad x \in \partial \Omega, \;t>0. \] The authors obtain an a posteriori error estimation of the approximate solutions using the method of the dual problem.