Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids

Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids

Hausdorff Center for Mathematics via YouTube Direct link

Summary of Part 4

18 of 20

18 of 20

Summary of Part 4

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Classroom Contents

Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids

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  1. 1 Intro
  2. 2 The outline
  3. 3 Motivation: Optimal transport
  4. 4 Motivation: Inverse reflector problem
  5. 5 Simple Monge Ampere equation
  6. 6 Ellipticity and convexity
  7. 7 Without convexity: Loss of uniqueness
  8. 8 Viscosity solution of the Monge Ampere equation
  9. 9 Summary of Part 1
  10. 10 Classical equivalence
  11. 11 Viscosity solutions of HJB
  12. 12 Equivalence in viscosity sense
  13. 13 Comparison principle
  14. 14 Summary of Part 2
  15. 15 Summary of Part 3
  16. 16 Towards convergence
  17. 17 How should we pose boundary conditions?
  18. 18 Summary of Part 4
  19. 19 Two numerical experiments
  20. 20 Summary of the presentation

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