Workshop on

numerical methods for multiscale problems

 

     
  Homepage  
  Program  
  Registration  
  Participants  
  Abstracts
  Arbogast  
  Bartels  
  Brokate  
  Conti  
  Eberhard  
  Eck  
  Flad  
  Forster  
  Graham  
  Griebel  
  Hackbusch  
  Hackl  
  Kaiser  
  Kastner  
  Kruzik  
  Lelievre  
  Melenk  
  Miehe  
  Sauter  
  Schneider  
  Weikard  
 
     
  Ulrich Weikard : Numerics of the Cahn-Hilliard model with inhomogeneous elasticity

Click here to see the abstract.
After introducing and motivating the Cahn--Hilliard model and its extension with inhomogeneous elasticity we present a fully discrete finite element approximation. \begin{eqnarray*} \frac{\partial \rho}{\partial t}&=& \Delta \Big(\psi^{\prime}(\rho) -\gamma\Delta \rho -\Spannung:\Equer^{\prime}(\rho) + (\E(\vecu)-\Equer(\rho)):\C^{\prime}(\rho)(\E(\vecu)-\Equer(\rho))\Big) , \\ 0 &=& \div \Spannung, \\ \Spannung &=& \C(\rho)(\E(\vecu)-\Equer(\rho)), \end{eqnarray*} where $\psi$ is the homogeneous free energy, $\Spannung$ the stress, $\E$ the strain and $\Equer(\rho)$ denotes the stress free strain at concentration $\rho$. In this model the elasticity tensor $\C$ depends on the concentration $\rho$. Additionally anisotropic effects can be incorporated via an appropriate choice of $\C$. We present the sketch of the proof of convergence of the finite element approximation. Numerical calculations with anisotropic, inhomogenous elasticity yield results that closely resemble experimental data. \par\bigskip Joint work with H. Garcke and M. Rumpf.
Impressum
  This page was last modified Wed Nov 6 18:31:42 2002 by Ronald Kriemann.   Best viewed with any browser