Neumann–Neumann algorithms for a mortar Crouzeix–Raviart element for 2nd order elliptic problems

The paper proposes two scalable variants of the Neumann–Neumann algorithm for the lowest order Crouzeix–Raviart finite element or the nonconforming P1 finite element on nonmatching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions, requiring function values only at the mesh interface nodes. The algorithms are analyzed using the abstract Schwarz framework, proving a convergence which is independent of the jumps in the coefficients of the problem and only depends logarithmically on the ratio between the subdomain size and the mesh size.