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Finite element method



16H45

The objectives are to present the mathematical foundations underlying the finite element method. The main stages of processing a problem defined by partial differential equations are described (boundary conditions, weak formulation, domain meshing, discretization, …). The course is aimed to make students aware of the difficulties caused by the mesh in the interpretations of results. The goal is not to know how to write a software that uses this method but to help understanding how finite element software operates.

PROGRAM :

  • Introduction : partial differential equations, domains, boundary conditions
  • Transition from continuous problem to algebraic equation : strong/weak formulation, sub-domains
  • Meshes and shape functions.
  • 1D theoretical problem treated in detail.
  • Application examples : finite elements within engineering problems.

The lectures are followed by practical work session.      
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