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Advanced Finite Element Analysis (AMMA)

Course Type: 
PhD Course
Academic Year: 
20 h

An advanced course dedicate to the analysis of finite element methods, as found in modern numerical analysis literature. A basic knowledge of Sobolev spaces is expected.

Detailed program

Review of basic results for Finite Element Analysis (Galerkin method) (2h)

  • Lax Milgram Lemma
  • Cea’s Lemma
  • Bramble Hilbert Lemma
  • Inverse estimates
  • Trace estimates

Non-conforming finite element methods (2h)

  • Strangs I and II Lemmas
  • Symmetric Interior Penalty method
  • Analysis of SIP DGFEM

Mixed and hybrid finite element methods (4h)

  • Mixed Laplace Problem
  • Stokes Problem
  • A priori error estimates (exploiting Strang Lemmas)
  • Proving the inf-sup (Fortin’s trick, macroelement technique)

Fluid structure interaction problems (2h)

  • Problem definition
  • Classical Finite Element Approximation: Arbitrary Lagrangian Eulerian Formulation

Immersed Boundary Method (2h)

  • Definition
  • Finite Difference Approximation
  • Dirac Delta Approximation

Immersed Finite Element Method (4h)

  • Definition
  • Analysis of IFEM - 1D simple case
  • Stability of IFEM (2D and 3D case)

Student projects (4h)

  • Short seminars from students, valid as exam
Next Lectures: 

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