Tutorial Part VI (Adaptive Solution of Time-Dependent Problems)

Adaptive hp-FEM with dynamical meshes for time-dependent PDE and PDE systems is one of the most advanced techniques in Hermes. Although we have published it in several scientific articles, there is still a lot of space for improvement. Do not see the results presented in this section as final.

• Nonlinear Parabolic Problem (01-timedep-adapt-space-only)
  • Model problem
  • Weak forms for the implicit Euler method
  • Weak forms for the Crank-Nicolson method
  • Problems with the Crank-Nicolson method
  • Starting the computation
  • Time stepping and periodic mesh derefinement
  • First time step only: solve on coarse mesh
  • Adaptivity loop
  • Sample results
• Heat and Moisture Transfer in Concrete (04-heat-and-moisture-adapt)
  • Model problem
  • Activation of multimesh assembling
  • Definition of time-dependent boundary conditions
  • Initialization of spaces
  • Definition of constant initial conditions
  • Registration of weak forms
  • Time stepping loop and periodic global derefinement
  • Creating globally refined reference meshes
  • Initializing matrix solver
  • Assembling and solving the reference mesh problem
  • Projecting reference solution on coarse meshes
  • Registering custom forms for error calculation
  • Calculating element errors and a global error estimate
  • Refining the meshes
  • End of time step: saving solutions for the next time step
  • Sample results
• Gross-Pitaevski Equation (05-gross-pitaevski-adapt)
  • Model problem
  • Sample results