• Methods with limited applicability: the Picard iteration method; the nonlinear Gauss-Seidel method
  
• The Newton iteration method; local convergence
  
• The damped Newton iteration method; global convergence, inner iteration stopping criteria; coupling of the method with adaptive mesh refinements
  
• The two-grid Newton method; rate of convergence
  
• Nonlinear conjugate gradient method

Prerequisites:
General knowledge on iterative solution methods, rate of convergence, conjugate gradient, multigrid methods.