Do We Have Spurious Modes in Non-Conformal Domain Decomposition Methods ?

This paper investigates the issue of spurious modes in the recent proposed non-conformal domain decomposition method. By consulting a recent publication by Buffa and Perugia, and validated through numerical experiments, we conclude that the non-conformal domain decomposition methods using Is order Robin transmission condition produce spurious-free approximations. Moreover, the convergence rate of the numerical approximations in non-conformal DDM is optimal, namely with p^th order mixed Nedelec elements on tetrahedral, we have O(h^p) and O(h^2p) for field solution and eigenvalues, respectively. Nonetheless, the Robin transmission condition is energy dissipative, and the amount of energy loss can be reduced by O(h^2p) by using finer discretizations on the domain interfaces.