Seminar Spectral Methods for PDEs


First meeting: April 10, 13:00 - 14:00 in Rogowski 328.


Spectral methods for PDEs are essentially Galerkin methods that use orthogonal basis functions. In the simplest cases, the convergence of the method is determined only by the smoothness of the exact solution. If the exact solution is arbitrarily smooth, then the method shows spectral convergence, i.e. convergence faster than any polynomial order. This is the main advantage of spectral methods, which also make them interesting for high-dimensional problems. In this seminar, we will deal with the basic theory, but will also discuss techniques to handle non-smooth solutions.

  • Hesthaven, Gottlieb, Gottlieb: Spectral Methods for Time-Dependent Problems, Cambridge University Press, 2006.
  • Selected papers

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