UN CO RR EC TE D PR O O F 1 A Neumann - Dirichlet Preconditioner for FETI - DP 2 Method for Mortar Discretization of a Fourth Order 3 Problems in 2 D 4

FETI-DP methods were introduced in [8]. They form a class of fast and efficient 13 iterative solvers for algebraic systems of equations arising from the finite element 14 discretizations of elliptic partial differential equations of second and fourth order, 15 cf. [8, 10, 11, 16] and references therein. In a one-level FETI-DP method one has 16 to solve a linear system for a set of dual variables formulated by eliminating all 17 primal unknowns. The FETI-DP system contains in itself a coarse problem, while 18 the preconditioner is usually fully parallel and constructed only from local problems. 19 There are many works investigating iterative solvers for mortar method for sec20 ond order problem, e.g. cf. [1–3] and references therein. There have also been a few 21 FETI-DP type algorithms developed for mortar discretization of second order prob22 lems, cf. e.g. [6, 7, 9]. But there is only a small number of studies focused on fast 23 solvers for mortar discretizations of fourth order elliptic problems, cf. [12, 15, 17]. 24 In this study we follow the approach of [9] which considers the case of a FETI-DP 25 method for mortar discretization of a second order problem. 26