Abstract
We present a C \begin{document}$ ^0 $\end{document} interior penalty method for the Cahn-Hilliard equation. We demonstrate that the numerical scheme is uniquely solvable, unconditionally energy stable, and convergent. We remark that the novelty of this paper lies in the fact that this is the first C \begin{document}$ ^0 $\end{document} interior penalty finite element method developed for the Cahn-Hilliard equation. Additionally, the error analysis presented develops a detailed methodology for analyzing time dependent problems utilizing the C \begin{document}$ ^0 $\end{document} interior penalty method. We furthermore support our conclusions with a few numerical experiments.
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