A new formulation for imposing dirichlet boundary conditions on non-matching meshes

Generating matching meshes for problems with complex boundaries is often an intricate process, and the use of non-matching meshes appears as an appealing solution. Yet, enforcing boundary conditions on non- matching meshes is not a straightforward process, especially when prescribing those of Dirichlet type. By combining a generalized finite element formulation with the Lagrange multiplier method, a new framework for the treatment of essential boundary conditions on non-matching meshes is introduced in this manuscript. The new formulation yields a symmetric stiffness matrix and is straightforward to implement. As a result, the methodology makes possible the analysis of problems with the use of simple structured meshes, irrespective of the problem domain boundary. Through the solution of linear elastic problems, we show that the optimal rate of convergence is preserved. Yet, the formulation is general and thus can be applied to any type of boundary value problem.