Benchmarks (Problems with Known Exact Solutions)

This section contains benchmarks with known exact solutions that are great for comparing adaptivity algorithms.

• Smooth-iso (Elliptic)
  • Model problem
  • Exact solution
  • Sample solution
  • Convergence comparisons
• Smooth-aniso-x (Elliptic)
  • Model problem
  • Exact solution
  • Convergence comparisons
• Smooth-aniso-y (Elliptic)
• L-Shape (Elliptic)
  • Model problem
  • Exact solution
  • Boundary conditions
  • Sample solution
  • Convergence comparisons
• Interior Layer (Elliptic)
  • Model problem
  • Exact solution
  • Right-hand side
  • Boundary conditions
  • Sample solution
  • Convergence comparison
• Boundary Layer (Elliptic)
  • Model problem
  • Exact solution
  • Right-hand side
  • Sample solution
  • Convergence comparison for isotropic refinements
  • Convergence comparison for anisotropic refinements
  • h-FEM (p=1): comparison of isotropic and anisotropic refinements
  • h-FEM (p=2): comparison of isotropic and anisotropic refinements
  • hp-FEM: comparison of isotropic and anisotropic refinements
• Two-Group Neutronics (Neutronics)
  • Model problem
  • Material properties
  • Boundary conditions
  • Exact solution
  • Right-hand side
  • Weak formulation
  • Sample results
  • Comparison of single/multi-mesh hp-FEM
  • Comparison of h-FEM (p=1), h-FEM (p=2) and hp-FEM with h-anisotropic refinements
  • Comparison of hp-FEM with iso, p-aniso, h-aniso and hp-aniso refinements
• Advection-reaction (Hyperbolic)
  • Model problem
  • Exact solution
  • Methods overview
  • Weak forms
  • Sample results
  • Convergence comparisons
  • References
• Non-symmetric (Elliptic)
  • Model problem
  • Exact solution
  • Sample solution
  • Convergence comparison
• Screen (Maxwell’s Equations)
  • Model problem
  • Boundary conditions
  • Exact solution
  • Sample solution
  • Convergence comparisons