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Masterthesis

If you use this code, please cite:

@misc{https://doi.org/10.48550/arxiv.2208.04242,
  doi = {10.48550/ARXIV.2208.04242},
  url = {https://arxiv.org/abs/2208.04242},  
  author = {Harder, Paula},
  title = {Abstract error analysis for Cahn--Hilliard type equations with dynamic boundary conditions},
  publisher = {arXiv},
  year = {2022}
}

This project are the implementations I did for my masterthesis. These implementations solve the Cahn-Hilliard equation with dynamic Cahn-Hilliard boundary conditions on a disk by using the finite element method for spatial discretization and the bdf3 method for time discretization. For details please read my thesis. You can contact me for questions: paulaharder@posteo.de

The directory /errorPlots/linearCase contains an implementation of solving a linear variant of the Cahn-Hilliard equation and generates error plots, to visualize the spatial convergence. To obtain the plot shown in my thesis just run the main_cahn_hilliard_linear.m file. This case needs about one hour to finish, if you want to have quicker results you need to decrease the variable number_of_grids

The directory /errorPlots/nonlinearCase contains an implementation of solving a linear variant of the Cahn-Hilliard equation and generates error plots, to visualize the spatial convergence. To obtain the plot shown in my thesis just run the main_cahn_hilliard_linear.m file. This case needs about one hour to finish, if you want to have quicker results you need to decrease the variable number_of_grids

The directory /evolutionPlot contains an implementation of solving a nonlinear variant of the Cahn-Hilliard equation and generates plots, to visualize the evolution of the solution in time. To obtain the plot shown in my thesis just run the main_evolution_plot.m file. This case needs about half an hour to finish, if you want to have quicker results you need to decrease the variable grid_number

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Solving Cahn-Hilliard with dynamic boundary conditions.

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