Adaptive hphp-FEM with dynamical meshes for transient heat and moisture transfer problems

We are concerned with the time-dependent multiphysics problem of heat and moisture transfer in the context of civil engineering applications. The problem is challenging due to its multiscale nature (temperature usually propagates orders of magnitude faster than moisture), different characters of the two fields (moisture exhibits boundary layers which are not present in the temperature field), extremely long integration times (30 years or more), and lack of viable error control mechanisms. In order to solve the problem efficiently, we employ a novel multimesh adaptive higher-order finite element method (hphp-FEM) based on dynamical meshes and adaptive time step control. We investigate the possibility to approximate the temperature and humidity fields on individual dynamical meshes equipped with mutually independent adaptivity mechanisms. Numerical examples related to a realistic nuclear reactor vessel simulation are presented.