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Numerical Analysis

Advanced Finite Element Analysis

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

A priori estimates (4h)

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

Stabilization mechanisms (2h)

Reduced Order Methods for Computational Mechanics

The course aims to provide the basic aspects of numerical approximation and efficient solution of parametrized; PDEs for computational mechanics problem (heat and mass transfer, linear elasticity, viscous and potential flows) using reduced order methods.

Advanced Programming

Provide advanced knowledge of both theoretical and practical programming in C ++ and Python, with particular regard to the principles of object oriented programming and best practices of software development (advanced use of version control systems, continuous integration, unit testing).

Syllabus:

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