Partial Differential Equations in Mechanics

The CIMPA research school "Partial Differential Equations in Mechanics" will focus on certain recent progress of mathematical analysis and numerical computations related to the partial differential equations namely to fluid mechanics for engineering science. Lectures aim to introduce advanced techniques for the numerical computation of solutions of several classes of PDEs. In particular finite element, finite difference and spectral methods, definition of numerical simulations for different models, comparison with the predictions of analytic results will be presented. A special attention will be given to the convergence of phase field models to sharp interface models for vanishing width of the diffusive interface in the phase field model and construction of asymptotic solutions. Some classes of partial differential equations are going from Stokes or Navier-Stokes equations, to those describing the option pricing. Also it will be introduced a treatment for the homogenization of an elastic Tresca friction problem.