Finite element programming by FreeFem++ -- intermediate course

• 1st lecture :
  Basics of finite element method from the Poisson equation
  
  • example1, page 7 poisson-mixedBC.edp : Poisson equation with both Dirichlet and Neumann boundary conditions.
    
  • example2, page 11 poisson-matrix.edp : FEM matrix from variational formulation with the same problem as example1.
    
  • example3, page 20 poisson-error.edp : convergence check of P2 finite element solution for the Poisson equation.
    
  • example4, page 21 poisson-buildmesh.edp : convergence check using unstructured mesh.
    
• 2nd lecture :
  Mixed formulation for the Stokes equations
  
  • example5, page 30 stokes-P2P1-error.edp : mixed formulation of Stokes equations with P2/P1 finite elements and error estimation.
    
  • example6, page 32 stokes-stabilized-error.edp : P1/P1 stabilized method.
    
  • example7, page 35 stokes-matrix.edp : usage of matrix and vector and treatment of inhomogenous Dirichlet boundary conditions.
    
• 3rd lecture :
  Nonlinear finite element problem by Newton method
  
  • example8, page 40 cavityNewton.edp : stationary cavity driven flow problem by Newton iteration.
    
• 4th lecture :
  Application of finite element method to flow problems
  • example9, page 49 NS-cylinder.edp : time-dependent Navier-Stokes equations by Characteristic Galerkin method
    
  • example10, page 55 RayleighBenard.edp : Rayleigh-Benard thermal convection in a box : time-dependent problem
    
  • example11, page 56 RayleighBenard-stat.edp : Rayleigh-Benard thermal convection in a box : stationary problem
    
• 5th lecture :
  Details on iterative linear solvers
  • example12, page 59 poisson-LinearCG.edp : conjugate gradient method with diagonal preconditioner.
    
  • example13, page 61 poisson-LinearCG-projection.edp : Poisson equation with full-Neumann boundary condition is solved by CG with orthogonal projection onto the image space.
    
  • example13b, page appx. poisson-Lagrange-mult.edp : Poisson equation with full-Neumann boundary condition is solved by Lagrange multiplier and UMFPACK direct solver.
    
  • example14, page 63 stokes-Uzawa.edp : CG method in Uzawa iteration for the Stokes equation with pressure ambiguity
    
  • example15, page 65 NS-cylinder-Uzawa.edp Uzawa-CG method with Cahouet-Chabard preconditioner for time dependent Navier-Stokes equations