A novel Lagrange-multiplier based method for consistent mesh tying

We propose a novel Lagrange-multiplier method for mesh tying in R² that passes a linear patch test for subdomains with non-coincident interfaces. This capability is required in contact problems and finite element analysis of complex bodies that were broken into simpler shapes to aid grid generation, and where independent descriptions of a shared curved boundary may not necessarily match. In mortar methods Lagrange multipliers are defined on one of the sides and field continuity is enforced by projecting data from the other side. For some interface configurations, this approach may fail to pass a linear patch test. In our method constraints express equilibrium of weighted field averages on the non-matching interfaces. As a result, selection of master and slave sides, a projection operator, or additional meshing are not required. Numerical results for several prototype mesh-tying problems illustrate the attractive computational properties of the new method.