The scope of problems accessible for a numerical treatment has been constantly broadened over the last fifty years. In particular, there has been a lot of research activity in the recent decades aimed at the problems with multi-scale and multi-physics features. The dedicated numerical methods (model reduction, micro-macro models and model coupling, non standard FEM) stem from diverse techniques and ideas such as homogenization, asymptotic analysis, statistical physics, domain decomposition methods, etc. In the same time, much effort has been devoted to the development of a posteriori error estimators which can now not only guide the computational mesh adaptation, but also help to choose the correct model or to minimize the number of iterations in the complicated multi-physics solution process. The courses in this school are aimed to cover the state of the art numerical approaches mentioned above and to present both the underlying mathematical ideas and the real life applications.
The main Research School will be preceded by a Preschool with an introduction to Finite Element Method (FEM) including conforming and non conforming variants, mixed FEM ; a posteriori error control including Goal-Oriented approaches and adaptive FEM ; stochastic computational methods and micro-macro approaches ; homogenization and optimal control. The main School will contain advanced courses on numerical homogenization techniques, optimal control, error estimation and mesh adaptivity for multi-physics problems, finite volume methods for dissipative problems, asymptotic models for thin structures, and computational statistical physics. The possible applications of these techniques are in porous media flows, fluid-structure interaction, multiphase and other complex flows, modelling of vesicles and red blood cells, financial mathematics etc.
Our principal target would be young mathematicians, preferably with a master’s degree in mathematics or applied mathematics. The courses will be taught in English.