Discretization Methods: Volume Coupling Methods

Philipp Farah, Anh-Tu Vuong and Alexander Popp

Strongly coupled multiphysical problems have been a field of extensive research over the last years. Nearly all developments are based on the assumption of matching finite element meshes for all involved physics. But that fact is, that each physic makes individual demands on mesh resolution and polynomial order of element shape functions. Therefore, volume coupling methods for non-matching finite element meshes are on focus of our research.

Instead of imposing volumetric coupling conditions in a strong, pointwise sense as in collocation methods, we employ a weak (weighted) enforcement in analogy to mortar methods. 

Typical applications at the Institute for Computational Mechanics are Thermo-Structure-Interaction problems and volumetrically coupled Fluid-Structure problems (porous media).