Teacher: Gianluigi Rozza

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

Contents include examples of elliptic and parabolic parametrized problems with several applications and examples in heat and mass transfer, linear elasticity, potential and viscous flows; efficient resolution of Parametrized PDEs with Reduced Basis method (RB); elements of a posteriori error estimation and error bounds for RB; affine and non-affine parametric dependence; some elements of approximation and algebraic stability; comparison with other reduced order modelling techniques (POD); some elements of optimization and control for complex parametrized systems