Git reference: Example saphir.
This is a standard nuclear engineering benchmark (IAEA number EIR-2) describing an external-force-driven configuration without fissile materials present, using one-group neutron diffusion approximation
(1)-\nabla \cdot (D(x,y) \nabla \Phi) + \Sigma_a(x,y) \Phi - Q_{ext}(x,y) = 0.
The domain of interest is a 96 x 86 cm rectangle consisting of five regions:
The unknown is the neutron flux \Phi(x, y). The values of the diffusion coefficient D(x, y), absorption cross-section \Sigma_a(x, y) and the source term Q_{ext}(x,y) are constant in the subdomains. The source Q_{ext} = 1 in areas 1 and 3 and zero elsewhere. Boundary conditions for the flux \Phi are zero everywhere.
This example uses multiple weak forms that are associated with different material markers.
Solution:
Final mesh (h-FEM with linear elements):
Final mesh (h-FEM with quadratic elements):
Final mesh (hp-FEM):
DOF convergence graphs:
CPU time convergence graphs: