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Stability and Error Analysis for a C$$^0$$ Interior Penalty Method for the Modified Phase Field Crystal Equation

https://doi.org/10.1007/s44007-024-00133-x

Diegel, Amanda E; Bond, Daniel; Sharma, Natasha S (December 2024, La Matematica)

We present a C^0 interior penalty finite element method for the sixth-order modified phase field crystal equation. We demonstrate that the numerical scheme is uniquely solvable, unconditionally energy stable, and convergent. Additionally, the error analysis presented develops a detailed methodology for analyzing time dependent problems utilizing the Cinterior penalty method. We furthermore support the theory with several numerical experiments.
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A C ⁰ interior penalty method for the phase field crystal equation

https://doi.org/10.1002/num.22976

Diegel, Amanda E.; Sharma, Natasha S. (May 2023, Numerical Methods for Partial Differential Equations)

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Unconditional Energy Stability and Solvability for a C0 Interior Penalty Method for a Sixth-Order Equation Modeling Microemulsions

https://doi.org/10.4208/ijnam2023-1019

null, Amanda E.; Sharma, Natasha S. (March 2022, International Journal of Numerical Analysis and Modeling)

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