Boundary conditions in Possion tutorial

General
1

This might be a stupid question but i’ve been stuck what does this code mean on link Implementation — FEniCSx tutorial
i want to know what are the conditions of this problem actually. it seems like it doesn’t specify the top, bottom, left and right borders like other problems. if someone can explain in detail, i’ll be very greatful

import numpy
# Create facet to cell connectivity required to determine boundary facets
tdim = domain.topology.dim
fdim = tdim - 1
domain.topology.create_connectivity(fdim, tdim)
boundary_facets = mesh.exterior_facet_indices(domain.topology)

boundary_dofs = fem.locate_dofs_topological(V, fdim, boundary_facets)
bc = fem.dirichletbc(uD, boundary_dofs)
2

The boundary condition is that u=u_D on all degrees of freedom at the boundary.

3

Could you explain or example in numbers becasue now i cannot imagine what is “on all degrees of freedom at boundary”

4

Your mesh consists of facets that is classified as being on the boundary if:

  1. A facet is only connected to a single cell.

For the example that we are considering, we are using a P1 finite element space where all degrees of freedom are located at vertices.

Every facet of a 2D (triangular or quadrilateral) mesh is a line segment consisting of two vertices.
Thus, for every facet located at the boundary, we find the corresponding vertices. For these vertices, we find the degrees of freedom associated with them, and apply the Dirichlet condition on these.