An adaptive multiscale hybrid-mixed method for the Oseen equations

A novel residual a posteriori error estimator for the Oseen equations achieves efficiency and reliability by including multilevel contributions in its construction. Originates from Multiscale Hybrid Mixed (MHM) method, combines residuals skeleton of first-level partition domain, along with element-wise approximations. The second-level is local infers accuracy multiscale basis computations as part MHM framework. Also, face-degrees freedom method shape induce new face-adaptive procedure on mesh’s only. As result, approach avoids re-meshing partition, which makes adaptive process affordable straightforward complex geometries. Several numerical tests assess theoretical results.