Interfacing nonmatching FEM discretizations

Current FEM research is heavily focused on the three "multis": multiconstituent, multiphysics and multiscale. The treatment of nonmatching mesh discretizations occurs in all three, as well as in classical problems such as contact and impact. In our work the coupling was done through a displacement frame interposed between the interface meshes. The frame is treated with a FEM discretization and “glued” to the meshes through Lagrange multipliers collocated at mesh-interface nodes. The discrete coupling equations are derived from a 4-field variational principle.

The approach is general and may be used to couple meshes of arbitrary geometry, discretization type (e.g., FEM and BEM) and even meshes of different physics (e.g., structure and fluids). The main example of the talk focuses on a simplified 2D plane-stress case that can be explained in detail. The Interface Patch Test requirement for preservation of constant stress states leads to an easily visualized condition, called the zero-moment rule or ZMR, that can be used to locate frame nodes on the frame geometry.