Tutorial Part C (Transient Problems)

In this part of the tutorial we will learn how to solve time-dependent problems, both using the Rothe’s method (i.e., building the time-integration method into the weak formulation), and Runge-Kutta methods defined in terms of arbitrary Butcher’s tables.

• Using the Implicit Euler Method (01-implicit-euler)
  • Model problem
  • Weak formulation
  • Defining weak forms
  • Passing and accessing previous time level solution
  • Keeping the Jacobian if it did not change
  • Sample results
• Using Arbitrary Runge-Kutta Methods (02-runge-kutta)
  • Runge-Kutta methods and Butcher’s tables
  • Butcher’s tables currently available in Hermes
  • Model problem
  • Weak formulation
  • Defining weak forms
  • Selecting a Butcher’s table
  • Initializing Runge-Kutta time stepping
  • Time-stepping loop
• Nonlinear Example (03-nonlinear)
  • Model problem
  • Weak formulation
  • Weak forms
  • Time stepping loop