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Numerical Solution of PDEs Using the Finite Element Method (AMMA, MHPC)

Lecturer: 
Luca Heltai, Martin Kronbichler
Course Type: 
PhD Course
Academic Year: 
2016-2017
Period: 
15-20 May 2017
Duration: 
20 h
Description: 

Advanced course dedicated to the Numerical Solution of Partial Differential Equations through the deal.II Finite Element Library.

Topics:

  • Recap on the Finite Element Method (Sobolev Spaces, Lax Milgram, Variational Formulations, Bramble Hilbert)
  • Relationship between the mathematical formulation and the data structures in the deal.II library (Triangulation, DoFHandler, Mapping, FiniteElement, etc.)
  • Discretization of Lipschitz domains (Manifold descriptors, Mesh generation, Mesh adaptation)
  • Solving the Poisson problem in two and three dimensions
  • Computing errors and convergence rates
  • High Order Finite Element Approximations
  • Adaptive Mesh Refinement and a posteriori error estimation
  • Solving PDEs on surfaces embedded in three dimensions
  • Parallel implementation of the Finite Element Method
Prerequisites: 
Average C++ programming skills.
Location: 
Old SISSA Miramare Building (via Beirut 3–4).

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