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Numerical Analysis

Advanced Topics in Numerical Modelling of PDEs: Part I

Part I: "Reduced Basis Methods and a Posteriori Error Bounds for Parametrized Partial Differential Equations", March 15-17, 2016, Lecturer Prof. Gianluigi Rozza, Tutorials Dr. Francesco Ballarin

Learning outcomes/Objectives:

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.

Module Description:

Applied Mathematics: an Introduction to Scientific Computing

  • Frontal Lectures (about 30h), Interleaved with Laboratories (about 30h): total 60h
  •  This course is shared between the PhD in Mathematical Analysis, Modeling, and Applications, the Master in High Performance Computing ( and the Laurea Magistrale in Matematica


Topics in Computational Fluid Dynamics


  • Introduction to CFD, examples.
  • Incompressible flows.
  • Numerical methods for potential and thermal flows
  • Numerical methods for viscous flows: steady Stokes equations
  • Discretization techniques for steady and unsteady Navier-Stokes equations.
  • Advanced optional topic (1): compressible flows.
  • Advanced optional topic (2): fluid and structure interaction.

Material will be provided during classes.

Advanced Topics in Numerical Solutions of PDEs

  • Isogeometric Analysis Techniques (LH)
  • Boundary Element Methods (LH)
  • Numerical Optimal Control of PDEs (GR)
  • Reduced Basis Methods in Computational Mechanics (GR)
  • Shape Optimization (optional)


Material will be provided during classes, a calendar with topics and organization will be given during the first lecture.


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