The Nitsche mortar method for matching grids in a mixed finite element method

It is well-known that nonmatching grids are often used in finite element methods. Usually, grids are being matched along lines or surfaces that divide a domain into subdomains. Such lines or surfaces are called interfaces. The interface matching means the satisfaction of some continuity conditions when crossing the interface. The direct matching procedures fall into three groups: methods that use Lagrangian multipliers, mortar-methods based on the Nitsche technique, and penalty methods.