Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transferring the Dirichlet trace across the interface, the others for the Neumann trace. In every subdomain the original problem is discretized by the finite element method, using a priori non-matching grids and piece-wise polynomials of different degree. In this paper we provide several interpretations of the method and we carry out its stability and convergence analysis, showing that INTERNODES exhibits optimal convergence rate with respect to the finite element sizes. Finally we propose an efficient algorithm for the solution of the corresponding algebraic system.