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Numerical Analysis

Advanced Programming

The course aims to provide advanced knowledge of both theoretical and practical programming in C++11 and Python3, with particular regard to the principles of object-oriented programming and best practices of software development.


Numerical Solution of PDEs Using the Finite Element Method

The Finite Element Method Using deal.II This is an intensive course that teaches how to use the finite element library deal.II ( you should be familiar with C/C++, and with the Unix command line. We'll cover the basics of Finite Element Methods, and go from solving the Laplace equation on a uniformly refined grid, to solving the same equation using adaptively refined grids, in parallel, on a supercomputer.Lectures will be structured in the following way:

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.


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