Lectures

Nabil Bedjaoui (France) and Joaquim Correia (Portugal): Hyperbolic Conservation Laws (HCL)

  • Introduction, models and their motivations (Traffic/Crowd Flow; Population Balance Eqs.; Image Processing)
  • Linear and non-linear advection, diffusion or dispersion
  • Characteristics, shocks, entropy and capillary-viscosity solution(s)
  • Simplification/approximation by hyperbolic PDE models: capillary-viscosity limits
  • A glance of numerical methods (front tracking; level set method; difference and finite volume methods)


Ankik Giri (India), Fernando da Costa (Portugal), Michael Grinfeld (UK): Coagulation-Fragmentation Models (CFM)

  • Overview of coagulation-fragmentation models
  • Discrete models, existence and uniqueness results
  • Mass conservation and gelation
  • Continuous models with non- and singular rates
  • Weak solutions, existence and uniqueness results
  • Sectional methods to solve coagulation models


Youcef Mammeri (France): Continuous Modelling of Lithium Batteries (CMLB)

  • Mass action law
  • Basics of electrochemistry
  • Transport of particles, electromigration, diffusion


Rama Bhargava, Rajesh Kumar, Neela Natraj (India) and MarĂ­lia Pires (Portugal): Numerical Methods for Partial Differential Equations (NMPDE)

  • Finite element method in blood flow
  • Finite volume method in population balance equations
  • Convergence and error analysis of finite volume and element methods
  • Mesh free methods