Lecture 11 of 'Advanced Numerical Methods' (wi4212)

• The following subjects are discussed:
  
  
  • accuracy in extrema
  • modified equations, Lax Wendroff, Beam Warming
  • 1-norm error in the vicinity of discontinuous solutions
  • linear equations with variable coefficients
  • general finite volume method, color equation, conservative equation
  • high resolution method, no second order accuracy
    
    
  Corresponding sections in the book: Section 8.3.4 to 8.7 and 9.1 to 9.5
  
  
• Exercises 8.5 and 9.1 can be made.
  
  
• Additional information
  
  
  • Animation of nonconservative advection equation examples (the color equation)