| Abstract: |
| We propose a numerical approximation method for the Cahn-Hilliard equation that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C0 interior penalty spatial discretization of the fourth order Cahn-Hilliard equation, together with a semi-implicit temporal discretization. We prove the method is long time stable and long time accurate, for arbitrarily inaccurate initial conditions, provided enough data measurements are incorporated into the simulation. Numerical experiments illustrate the effectiveness of the method on a benchmark test problem. |
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