The three-field formulation for elasticity problems

The three-field decomposition method is particularly suited for decompositions with nonmatching grids. It corresponds to introduce an additional grid (usually uniform, or “easy”) at the interface. The unknown is then represented independently in each subdomain and on the interface. The matching between its value in each subdomain and on the interface is provided by suitable Lagrange multipliers. Here we discuss the main features of the method for a linear three-dimensional elasticity problem, in the simplest case of two subdomains. An easy numerical test to check whether the inf-sup conditions (necessary for the stability) are satisfied is also presented.