2018/02/21 by Simone Deparis, Deparis, Simone, Luca Pegolotti +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Numerical methods for differential equations #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1802.07601
openalex publication_date 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This work focuses on the development of a non-conforming domain decomposition\nmethod for the approximation of PDEs based on weakly imposed transmission\nconditions: the continuity of the global solution is enforced by a discrete\nnumber of Lagrange multipliers defined over the interfaces of adjacent\nsubdomains. The method falls into the class of primal hybrid methods, which\nalso include the well-known mortar method. Differently from the mortar method,\nwe discretize the space of basis functions on the interface by spectral\napproximation independently of the discretization of the two adjacent domains;\none of the possible choices is to approximate the interface variational space\nby Fourier basis functions. As we show in the numerical simulations, our\napproach is well-suited for the solution of problems with non-conforming meshes\nor with finite element basis functions with different polynomial degrees in\neach subdomain. Another application of the method that still needs to be\ninvestigated is the coupling of solutions obtained from otherwise incompatible\nmethods, such as the finite element method, the spectral element method or\nisogeometric analysis.\n