Explanation
This code solves a Poisson equation using the finite element method in FEniCS. The equation and boundary conditions are defined on a mesh read from an HDF5 file. The solution is written to another HDF5 file.
The Poisson equation is defined as:
\(-\nabla \cdot (d_poi_0 \nabla u) = f_poi_0\)
where \(d_poi_0\) and \(f_poi_0\) are constants, and \(u\) is the unknown function.
The finite element space used for the solution is a piecewise linear function space on the mesh. The bilinear form is formed by multiplying the trial function with the test function and integrating over the domain. The linear form is simply the source term multiplied by the test function and integrated over the domain.
The boundary conditions are specified using Dirichlet boundary conditions, where a constant value of zero or -0.1 is imposed on certain subdomains of the boundary.
Finally, the solve() function is called to solve for the unknown function u subject to the given boundary conditions and source term. The solution is then written to an HDF5 file.
