Actually I am very new to fenics , And i was curious about why don’t we use any boundary conditions in Cahn Hillard equation( from the documentation) like we use for diffusion equation or Poissons equation
In Cahn-Hilliard equation — DOLFINx 0.5.1 documentation
you can see that if you integrate the divergence operators by parts.
Then you get the formulas stated as boundary conditions, equal to zero. This is called a natural boundary condition.
Does this mean that we don’t have to specify the boundary conditions in Cahn-Hillard Equation.
And what if we have multiple boundaries like neuman and dirichlet in this case .
Does this make sense or not
If you use the boundary conditions in the demo, you do not need to specifying them (by removing the boundary integral you are implicitly setting them). If you set Dirichlet boundary condtions, or non-homogeneous Neumann or Robin type condition, you either need to specify them explicity as DirichletBC, or add extra terms to the variational form.
Thank you .
Although I am still curious like what is the physical meaning of these boundary conditions which are specified in the demo version.
And like when we say these are natural boundary conditions what is the physical sense of it.