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Numerical Solution of PDEs

Course Type: 
PhD Course
Academic Year: 
February - April
40 h

This course provides a high level overview on the numerical solution of partial differential equations. All major classes of numerical methods will be analysed within a rigorous mathematical setting. Key aspects, such as consistency and stability, will be thoroughly investigated, providing the guidelines for the correct choice and implementation of numerical methods for a range of problems.

The lectures will be completed by a series of guided problems for testing in practice the numerical algorithms and their properties, helping everyone to build their own suits of simulation codes. 

This course is suitable for students pursuing a research career in numerical analysis as well as students that may just use PDE models in their research.


  1. Problems of mathematical physics
  2. Numerical ODEs
  3. Finite Difference Methods
  4. Consistency, stability and convergence
  5. Dispersion, dissipation
  6. Solution of the discrete systems arising from numerical PDEs
  7. Functional spaces, weak problems
  8. Finite Element Methods (FEM) for elliptic problems
  9. Convergence analysis
  10. Variational crimes and Strang's Lemmas
  11. Stable discretisation of convection-diffusion problems
  12. FEM for evolution problems
  13. Conservation laws 
  14. Finite Volume method
  15. DG time-stepping
  16. Other methods
  17. Other problems
also on Zoom
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