Theophile Chaumont Frelet, Diego Paredes, Frederic Valentin:
Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods
The flux variable determines the approximation quality of hybridization-based numerical methods. This work proves that approximating flux variables in discontinuous polynomial spaces from the L2 orthogonal projection is super-convergent on meshes that are not necessarily aligned with jumping coefficient interfaces. The results assume only the local regularity of exact solutions in physical partitions. Based on the proposed flux approximation, we demonstrate that the mixed hybrid multiscale (MHM) finite element method is superconvergent on unfitted meshes, supporting the numerics presented in MHM seminal works.