Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space.

This work focuses on the development of a non-conforming domain decompositionmethod for the approximation of PDEs based on weakly imposed transmissionconditions: the continuity of the global solution is enforced by a discretenumber of Lagrange multipliers defined over the interfaces of adjacentsubdomains. The method falls into the class of primal hybrid methods, whichalso include the well-known mortar method. Differently from the mortar method,we discretize the space of basis functions on the interface by spectralapproximation independently of the discretization of the two adjacent domains;one of the possible choices is to approximate the interface variational spaceby Fourier basis functions. As we show in the numerical simulations, ourapproach is well-suited for the solution of problems with non-conforming meshesor with finite element basis functions with different polynomial degrees ineach subdomain. Another application of the method that still needs to beinvestigated is the coupling of solutions obtained from otherwise incompatiblemethods, such as the finite element method, the spectral element method orisogeometric analysis.